Selina Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 16 Understanding Shapes (Including Polygons)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 16 Understanding Shapes (Including Polygons)

Understanding Shapes Exercise 16A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
State which of the following are polygons :

If the given figure is a polygon, name it as convex or concave.
Solution:

Question 2.
Calculate the sum of angles of a polygon with :
(i) 10 sides
(ii) 12 sides
(iii) 20 sides
(iv) 25 sides
Solution:

Question 3.
Find the number of sides in a polygon if the sum of its interior angles is :
(i) 900°
(ii) 1620°
(iii) 16 right-angles
(iv) 32 right-angles.
Solution:

Question 4.
Is it possible to have a polygon ; whose sum of interior angles is :
(i) 870°
(ii) 2340°
(iii) 7 right-angles
(iv) 4500°
Solution:

Question 5.
(i) If all the angles of a hexagon are equal ; find the measure of each angle.
(ii) If all the angles of a 14-sided figure are equal ; find the measure of each angle.
Solution:

Question 6.
Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with :
(i) 7 sides
(ii) 10 sides
(iii) 250 sides.
Solution:

Question 7.
The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x – 1)°, (10x + 2)°, (8x + 2)° (9x – 3)°, (5x + 4)° and (12x + 6)° ; find each exterior angle.
Solution:

Question 8.
The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.
Solution:

Question 9.
Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.
Solution:

Question 10.
The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.

(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E
(iii) Find angles B, C and D.
Solution:

Question 11.
Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.
Solution:

Question 12.
In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.
Solution:

Question 13.
the angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°. Find x.
Solution:

Question 14.
In a pentagon, two angles are 40° and 60°, and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.
Solution:

Understanding Shapes Exercise 16B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Fill in the blanks :
In case of regular polygon, with :

Solution:

Question 2.
Find the number of sides in a regular polygon, if its each interior angle is :
(i) 160°
(ii) 135°
(iii) \(1\frac { 1 }{ 5 }\) of a right-angle
Solution:

Question 3.
Find the number of sides in a regular polygon, if its each exterior angle is :
(i) \(\frac { 1 }{ 3 }\) of a right angle
(ii) two-fifth of a right-angle.
Solution:

Question 4.
Is it possible to have a regular polygon whose each interior angle is :
(i) 170°
(ii) 138°
Solution:

Question 5.
Is it possible to have a regular polygon whose each exterior angle is :
(i) 80°
(ii) 40% of a right angle.
Solution:

Question 6.
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
Solution:

Question 7.
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
Solution:

Question 8.
The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :
(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.
Solution:

Question 9.
The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :
(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon
Solution:

Question 10.
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
Solution:

Question 11.
The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.
Solution:

Question 12.
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
Solution:

Question 13.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
Solution:

Question 14.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
Solution:

Question 15.
The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. Find the value of n.
Solution:

Question 16.
If the difference between the exterior angle of a n sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Solution:

Question 17.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Solution:

Question 18.
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
Solution:

Question 19.
Calculate the number of sides of a regular polygon, if:
(i) its interior angle is five times its exterior angle.
(ii) the ratio between its exterior angle and interior angle is 2 : 7.
(iii) its exterior angle exceeds its interior angle by 60°.
Solution:

Question 20.
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
Solution:

Understanding Shapes Exercise 16C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:

Question 3.
Angles of a quadrilateral are (4x)°, 5(x + 2)°, (7x – 20)° and 6(x + 3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C

Solution:

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD
Solution:

Question 6.
From the following figure find ;
(i) x
(ii) ∠ABC
(iii) ∠ACD
Solution:

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a + 2)° and ∠B = 2(2a + 7)°.
Calculate ∠A.
Solution:

Question 8.
In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.

Solution:

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.
Solution:

Question 11.
Use the informations given in the following figure to find the value of x.

Solution:

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Solution:

Question 13.
Use the following figure to find the value of x

Solution:

Question 14.
ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC = 90°.
Solution:

Question 15.
In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively. Show that:
∠AOB = \(\frac { 1 }{ 2 }\) (∠C + ∠D)
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 15 Linear Inequations (Including Number Lines)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 15 Linear Inequations (Including Number Lines)

Linear Inequations Exercise 15A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
If the replacement set is the set of natural numbers, solve.
(i) x – 5 < 0
(ii) x + 1 < 7
(iii) 3x – 4 > 6
(iv) 4x + 1 > 17
Solution:

Question 2.
If the replacement set = {-6, -3, 0, 3, 6, 9}; find the truth set of the following:
(i) 2x – 1 > 9
(ii) 3x + 7 < 1
Solution:

Question 3.
Solve 7 > 3x – 8; x ∈ N
Solution:

Question 4.
-17 < 9y – 8 ; y ∈ Z
Solution:

Question 5.
Solve 9x – 7 ≤ 28 + 4x; x ∈ W
Solution:

Question 6.
Solve : \(\frac { 2 }{ 3 }\)x + 8 < 12 ; x ∈ W
Solution:

Question 7.
Solve -5 (x + 4) > 30 ; x ∈ Z
Solution:

Question 8.
Solve the inquation 8 – 2x > x – 5 ; x ∈ N.
Solution:

Question 9.
Solve the inequality 18 – 3 (2x – 5) > 12; x ∈ W.
Solution:

Question 10.
Solve : \(\frac { 2x+1 }{ 3 }\) + 15 < 17; x ∈ W.
Solution:

Question 11.
Solve : -3 + x < 2, x ∈ N
Solution:

Question 12.
Solve : 4x – 5 > 10 – x, x ∈ {0, 1, 2, 3, 4, 5, 6, 7}
Solution:

Question 13.
Solve : 15 – 2(2x – 1) < 15, x ∈ Z.
Solution:

Question 14.
Solve : \(\frac { 2x+3 }{ 5 }\) > \(\frac { 4x-1 }{ 2 }\) , x ∈ W.
Solution:

Linear Inequations Exercise 15B – Selina Concise Mathematics Class 8 ICSE Solutions

Solve and graph the solution set on a number line :
Question 1.
x – 5 < -2 ; x ∈ N
Solution:

Question 2.
3x – 1 > 5 ; x ∈ W
Solution:

Question 3.
-3x + 12 < -15 ; x ∈ R.
Solution:

Question 4.
7 > 3x – 8 ; x ∈ W
Solution:

Question 5.
8x – 8 < – 24 ; x ∈ Z
Solution:

Question 6.
8x – 9 > 35 – 3x ; x ∈ N
Solution:

Question 7.
5x + 4 > 8x – 11 ; x ∈ Z
Solution:

Question 8.
\(\frac { 2x }{ 5 }\) + 1 < -3 ; x ∈ R
Solution:

Question 9.
\(\frac { x }{ 2 }\) > -1 + \(\frac { 3x }{ 4 }\) ; x ∈ N
Solution:

Question 10.
\(\frac { 2 }{ 3 }\) x + 5 ≤ \(\frac { 1 }{ 2 }\) x + 6 ; x ∈ W
Solution:

Question 11.
Solve the inequation 5(x – 2) > 4 (x + 3) – 24 and represent its solution on a number line.
Given the replacement set is {-4, -3, -2, -1, 0, 1, 2, 3, 4}.
Solution:

Question 12.
Solve \(\frac { 2 }{ 3 }\) (x – 1) + 4 < 10 and represent its solution on a number line.
Given replacement set is {-8, -6, -4, 3, 6, 8, 12}.
Solution:

Question 13.
For each inequation, given below, represent the solution on a number line :
(i) \(\frac { 5 }{ 2 }\) – 2x ≥ \(\frac { 1 }{ 2 }\) ; x ∈ W
(ii) 3(2x – 1) ≥ 2(2x + 3), x ∈ Z
(iii) 2(4 – 3x) ≤ 4(x – 5), x ∈ W
(iv) 4(3x + 1) > 2(4x – 1), x is a negative integer
(v) \(\frac { 4 – x }{ 2 }\) < 3, x ∈ R
(vi) -2(x + 8) ≤ 8, x ∈ R
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 14 Linear Equations in one Variable (With Problems Based on Linear equations)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 14 Linear Equations in one Variable (With Problems Based on Linear equations)

Linear Equations in one Variable Exercise 14A – Selina Concise Mathematics Class 8 ICSE Solutions

Solve the following equations:
Question 1.
20 = 6 + 2x
Solution:

Question 2.
15 + x = 5x + 3
Solution:

Question 3.
\(\frac { 3x+2 }{ x-6 }\) = -7
Solution:

Question 4.
3a – 4 = 2(4 – a)
Solution:

Question 5.
3(b – 4) = 2(4 – b)
Solution:

Question 6.
\(\frac { x+2 }{ 9 } =\frac { x+4 }{ 11 }\)
Solution:

Question 7.
\(\frac { x-8 }{ 5 } =\frac { x-12 }{ 9 }\)
Solution:

Question 8.
5(8x + 3) = 9(4x + 7)
Solution:

Question 9.
3(x + 1) = 12 + 4(x – 1)
Solution:

Question 10.
\(\frac { 3x }{ 4 } -\frac { 1 }{ 4 } \left( x-20 \right) =\frac { x }{ 4 } +32\)
Solution:

Question 11.
\(3a-\frac { 1 }{ 5 } =\frac { a }{ 5 } +5\frac { 2 }{ 5 }\)
Solution:

Question 12.
\(\frac { x }{ 3 } -2\frac { 1 }{ 2 } =\frac { 4x }{ 9 } -\frac { 2x }{ 3 }\)
Solution:

Question 13.
\(\frac { 4\left( y+2 \right) }{ 5 } =7+\frac { 5y }{ 13 }\)
Solution:

Question 14.
\(\frac { a+5 }{ 6 } -\frac { a+1 }{ 9 } =\frac { a+3 }{ 4 }\)
Solution:

Question 15.
\(\frac { 2x-13 }{ 5 } -\frac { x-3 }{ 11 } =\frac { x-9 }{ 5 } +1\)
Solution:

Question 16.
6(6x – 5) – 5 (7x – 8) = 12 (4 – x) + 1
Solution:

Question 17.
(x – 5) (x + 3) = (x – 7) (x + 4)
Solution:

Question 18.
(x – 5)² – (x + 2)² = -2
Solution:

Question 19.
(x – 1) (x + 6) – (x – 2) (x – 3) = 3
Solution:

Question 20.
\(\frac { 3x }{ x+6 } -\frac { x }{ x+5 } =2\)
Solution:

Question 21.
\(\frac { 1 }{ x-1 } +\frac { 2 }{ x-2 } =\frac { 3 }{ x-3 }\)
Solution:

Question 22.
\(\frac { x-1 }{ 7x-14 } =\frac { x-3 }{ 7x-26 }\)
Solution:

Question 23.
\(\frac { 1 }{ x-1 } -\frac { 1 }{ x } =\frac { 1 }{ x+3 } -\frac { 1 }{ x+4 }\)
Solution:

Question 24.
Solve: \(\frac { 2x }{ 3 } -\frac { x-1 }{ 6 } +\frac { 7x-1 }{ 4 } =2\frac { 1 }{ 6 }\)
Hence, find the value of ‘a’, if \(\frac { 1 }{ a }\) + 5x = 8.
Solution:

Question 25.
Solve: \(\frac { 4-3x }{ 5 } +\frac { 7-x }{ 3 } +4\frac { 1 }{ 3 } =0\)
Hence find the value of ‘p’ if 2p – 2x + 1 = 0
Solution:

Question 26.
Solve: \(0.25+\frac { 1.95 }{ x } =0.9\)
Solution:

Question 27.
Solve: \(5x-\left( 4x+\frac { 5x-4 }{ 7 } \right) =\frac { 4x-14 }{ 3 }\)
Solution:

Linear Equations in one Variable Exercise 14B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Fifteen less than 4 times a number is 9. Find the number.
Solution:

Question 2.
If Megha’s age is increased by three times her age, the result is 60 years. Find her age
Solution:

Question 3.
28 is 12 less than 4 times a number. Find the number.
Solution:

Question 4.
Five less than 3 times a number is -20. Find the number.
Solution:

Question 5.
Fifteen more than 3 times Neetu’s age is the same as 4 times her age. How old is she?
Solution:

Question 6.
A number decreased by 30 is the same as 14 decreased by 3 times the number; Find the number.
Solution:

Question 7.
A’s salary is same as 4 times B’s salary. If together they earn Rs.3,750 a month, find the salary of each.
Solution:

Question 8.
Separate 178 into two parts so that the first part is 8 less than twice the second part.
Solution:

Question 9.
Six more than one-fourth of a number is two-fifth of the number. Find the number.
Solution:

Question 10.
The length of a rectangle is twice its width. If its perimeter is 54 cm; find its length.
Solution:

Question 11.
A rectangle’s length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm; the perimeter of the resulting rectangle will be 74 cm. Find the length and the width of the origi¬nal rectangle.
Solution:

Question 12.
The sum of three consecutive odd numbers is 57. Find the numbers.
Solution:

Question 13.
A man’s age is three times that of his son, and in twelve years he will be twice as old as his son would be. What are their present ages.
Solution:

Question 14.
A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?
Solution:

Question 15.
A man completed a trip of 136 km in 8 hours. Some part of the trip was covered at 15 km/hr and the remaining at 18 km/hr. Find the part of the trip covered at 18 km/hr.
Solution:

Question 16.
The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.
Solution:

Question 17.
Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.
Solution:

Question 18.
Three consecutive whole numbers are such that if they are divided by 5, 3 and 4 respectively; the sum of the quotients is 40. Find the numbers.
Solution:

Question 19.
If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.
Solution:

Question 20.
The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages.
Solution:

Linear Equations in one Variable Exercise 14C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Solve:
(i) \(\frac { 1 }{ 3 } x-6=\frac { 5 }{ 2 }\)
(ii) \(\frac { 2x }{ 3 } -\frac { 3x }{ 8 } =\frac { 7 }{ 12 }\)
(iii) (x + 2)(x + 3) + (x – 3)(x – 2) – 2x(x + 1) = 0
(iv) \(\frac { 1 }{ 10 } -\frac { 7 }{ x } =35\)
(v) 13(x – 4) – 3(x – 9) – 5(x + 4) = 0
(vi) x + 7 – \(\frac { 8x }{ 3 } =\frac { 17x }{ 6 } -\frac { 5x }{ 8 }\)
(vii) \(\frac { 3x-2 }{ 4 } -\frac { 2x+3 }{ 3 } =\frac { 2 }{ 3 } -x\)
(viii) \(\frac { x+2 }{ 6 } -\left( \frac { 11-x }{ 3 } -\frac { 1 }{ 4 } \right) =\frac { 3x-4 }{ 12 }\)
(ix) \(\frac { 2 }{ 5x } -\frac { 5 }{ 3x } =\frac { 1 }{ 15 }\)
(x) \(\frac { x+2 }{ 3 } -\frac { x+1 }{ 5 } =\frac { x-3 }{ 4 } -1\)
(xi) \(\frac { 3x-2 }{ 3 } +\frac { 2x+3 }{ 2 } =x+\frac { 7 }{ 6 }\)
(xii) \(x-\frac { x-1 }{ 2 } =1-\frac { x-2 }{ 3 }\)
(xiii) \(\frac { 9x+7 }{ 2 } -\left( x-\frac { x-2 }{ 7 } \right) =36\)
(xiv) \(\frac { 6x+1 }{ 2 } +1=\frac { 7x-3 }{ 3 }\)
Solution:

Question 2.
After 12 years, I shall be 3 times as old as 1 was 4 years ago. Find my present age.
Solution:

Question 3.
A man sold an article for 7396 and gained 10% on it. Find the cost price of the article
Solution:

Question 4.
The sum of two numbers is 4500. If 10% of one number is 12.5% of the other, find the numbers.
Solution:

Question 5.
The sum of two numbers is 405 and their ratio is 8 : 7. Find the numbers.
Solution:

Question 6.
The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.
Solution:

Question 7.
Find the number whose double is 45 greater than its half.
Solution:

Question 8.
The difference between the squares of two consecutive numbers is 31. Find the numbers.
Solution:

Question 9.
Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.
Solution:

Question 10.
The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes \(\frac { 2 }{ 3 }\). Find the original fraction.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

Algebraic Identities Exercise 12A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Use direct method to evaluate the following products :
(i) (x + 8)(x + 3)
(ii) (y + 5)(y – 3)
(iii) (a – 8)(a + 2)
(iv) (b – 3)(b – 5)
(v) (3x – 2y)(2x + y)
(vi) (5a + 16)(3a – 7)
(vii) (8 – b) (3 + b)
Solution:

Question 2.
Use direct method to evaluate :

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Use the product (a + b) (a – b) = a² – b² to evaluate:
(i) 21 × 19
(ii) 33 × 27
(iii) 103 × 97
(iv) 9.8 × 10.2
(v) 7.7 × 8.3
(vi) 4.6 × 5.4
Solution:

Question 5.
Evaluate :
(i) (6 – xy) (6 + xy)

Solution:

Algebraic Identities Exercise 12B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Expand :
(i) (2a + b)²
(ii) (a – 2b)²

Solution:

Question 2.
Find the square of :

Solution:

Question 3.
Evaluate:
Using expansion of (a + b)² or (a – b)²
(i) (208)²
(ii) (92)²
(iii)(415)²
(iv) (188)²
(v) (9.4)²
(vi) (20.7)²
Solution:

Question 4.
Expand :

Solution:

Question 5.
Find the cube of :

Solution:

Algebraic Identities Exercise 12C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
If a  +b = 5 and ab = 6; find a² + b²
Solution:

Question 2.
If a – b = 6 and ab = 16; find a² + b²
Solution:

Question 3.
If a² + b² = 29 and ab = 10 ; find :
(i) a + b
(ii) a – b
Solution:

Question 4.
If a² + b² = 10 and ab = 3; find :
(i) a – b
(ii) a + b
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
If a + b + c = 10 and a² + b² + c² = 38; find ab + bc + ca
Solution:

Question 10.
Find a² + b² + c² ; if a + b + c = 9 and ab + bc + ca = 24
Solution:

Question 11.
Find a + b + c; if a² + b² + c² = 83 and ab + bc + ca = 71
Solution:

Question 12.
If a + b = 6 and ab=8; find a³ + b³
Solution:

Question 13.
If a – b = 3 and ab = 10; find a³ – b³
Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
Solution:

Algebraic Identities Exercise 12D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Evaluate:

Solution:

Question 3.
Find the square of :

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.
If a² + b² = 41 and ab = 4, find :
(i) a – b
(ii) a + b
Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
Expand :
(i) (3x – 4y + 5z)²
(ii) (2a – 5b – 4c)²
(iii) (5x + 3y)³
(iv) (6a – 7b)³
Solution:

Question 10.
If a + b + c = 9 and ab + bc + ca = 15, find: a² + b² + c².
Solution:

Question 11.
If a + b + c = 11 and a² + b² + c² = 81, find ab + bc + ca.
Solution:

Question 12.
If 3x – 4y = 5 and xy = 3, find : 27x³ – 64y³.
Solution:

Question 13.
If a + b = 8 and ab = 15, find : a³ + b³.
Solution:

Question 14.
If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³
Solution:

Question 15.
If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³
Solution:

Question 16.
The difference between two numbers is 5 and their products is 14. Find the difference between their cubes.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation

Factorisation Exercise 13A – Selina Concise Mathematics Class 8 ICSE Solutions

Factorise :
Question 1.
15x + 5
Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Factorisation Exercise 13B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Factorise : a² + ax + ab + bx
Solution:

Question 2.
Factorise : a² – ab – ca + bc
Solution:

Question 3.
Factorise : ab – 2b + a² – 2a
Solution:

Question 4.
Factorise : a³ – a² + a – 1
Solution:

Question 5.
Factorise : 2a – 4b – xa + 2bx
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Factorisation Exercise 13C – Selina Concise Mathematics Class 8 ICSE Solutions

Note : a² – b² = (a + b) (a – b)
Question 1.
Factorise : 16 – 9x²
Solution:

Question 2.
Factorise : 1 – 100a²
Solution:

Question 3.
Factorise : 4x² – 81y²
Solution:

Question 4.

Solution:

Question 5.
Factorise : (a+2b)² – a²
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.
Evaluate :

Solution:

Question 15.
Evaluate :
(0.7)² – (0.3)²
Solution:

Question 16.
Evaluate :
(4.5)² – (1.5)²
Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Factorisation Exercise 13D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Factorisation Exercise 13E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
In each case find whether the trinomial is a perfect square or not:

Solution:

Question 2.
Factorise completely 2 – 8x².
Solution:

Question 3.
Factorise completely : 8x²y – 18y³
Solution:

Question 4.
Factorise completely : ax² – ay²
Solution:

Question 5.
Factorise completely : 25x³ – x
Solution:

Question 6.
Factorise completely : a⁴ – b⁴
Solution:

Question 7.
Factorise completely : 16x⁴ – 81y⁴
Solution:

Question 8.
Factorise completely : 625 – x⁴
Solution:

Question 9.
Factorise completely : x² – y² – 3x – 3y
Solution:

Question 10.
Factorise completely : x² – y² – 2x + 2y
Solution:

Question 11.
Factorise completely : 3x² + 15x – 72
Solution:

Question 12.
Factorise completely : 2a² – 8a – 64
Solution:

Question 13.
Factorise completely : 5b² + 45b + 90
Solution:

Question 14.
Factorise completely : 3x²y + 11xy + 6y
Solution:

Question 15.
Factorise completely : 5ap² + 11ap + 2a
Solution:

Question 16.
Factorise completely : a² + 2ab + b² – c²
Solution:

Question 17.
Factorise completely : x² + 6xy + 9y² + x + 3y
Solution:

Question 18.
Factorise completely : 4a² – 12ab + 9b² + 4a – 6b
Solution:

Question 19.
Factorise completely : 2a²b² – 98b⁴
Solution:

Question 20.
Factorise completely : a² – 16b² – 2a – 8b
Solution:

Factorisation Exercise 13F – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Factorise :

Solution:

Question 2.
Factorise :

Solution:

Question 3.
Factorise :

Solution:

Question 4.
Factorise :

Solution:

Question 5.
Factorise :

Solution:

Question 6.
Factorise :


Solution:

Question 7.
Factorise xy² – xz², Hence, find the value of:

Solution:

Question 8.
Factorise :

Solution:

Question 9.
Factorise a²b – b³ Using this result, find the value of 101² × 100 – 100³.
Solution:

Question 10.
Evaluate (using factors): 301² × 300 – 300³.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 7 Percent and Percentage

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 7 Percent and Percentage

Percent and Percentage Exercise 7A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate :
(i) 55% of 160 + 24% of 50 – 36% of 150
(ii) 9.3% of 500 – 4.8% of 250 – 2.5% of 240
Solution:

Question 2.
(i) A number is increased from 125 to 150; find the percentage increase.
(ii) A number is decreased from 125 to 100; find the percentage decrease.
Solution:

Question 3.
Find :
(i) 45 is what percent of 54?
(ii) 2.7 is what percent of 18?
Solution:

Question 4.
(i) 252 is 35% of a certain number, find the number.
(ii) If 14% of a number is 315; find the number.
Solution:

Question 5.
Find the percentage change, when a number is changed from :
(i) 80 to 100
(ii) 100 to 80
(iii) 6.25 to 7.50
Solution:

Question 6.
An auctioneer charges 8% for selling a house. If a house is sold for Rs.2, 30, 500; find the charges of the auctioneer.
Solution:

Question 7.
Out of 800 oranges, 50 are rotten. Find the percentage of good oranges.
Solution:

Question 8.
A cistern contains 5 thousand litres of water. If 6% water is leaked. Find how many litres of water are left in the cistern.
Solution:

Question 9.
A man spends 87% of his salary. If he saves Rs.325; find his salary.
Solution:

Question 10.
(i) A number 3.625 is wrongly read as 3.265; find the percentage error.
(ii) A number 5.78 × 10³ is wrongly written as 5.87 × 10³; find the percentage error
Solution:

Question 11.
In an election between two candidates, one candidate secured 58% of the votes polled and won the election by 18, 336 votes. Find the total number of votes polled and the votes secured by each candidate.
Solution:

Question 12.
In an election between two candidates, one candidate secured 47% of votes polled and lost the election by 12, 366 votes. Find the total votes polled and die votes secured by the winning candidate.
Solution:

Question 13.
The cost of a scooter depreciates every year by 15% of its value at the beginning of the year. If the present cost of the scooter is
₹ 8,000; find its cost:
(i) after one year
(ii) after 2 years
Solution:

Question 14.
In an examination, the pass mark is 40%. If a candidate gets 65 marks and fails by 3 marks; find the maximum marks.
Solution:

Question 15.
In an examination, a candidate secured 125 marks and failed by 15 marks. If the pass percentage was 35 %; find the maximum marks.
Solution:

Question 16.
In an objective type paper of 150 questions; John got 80% correct answers and Mohan got 64% correct answers.
(i) How many correct answers did each get?
(ii) What percent is Mohan’s correct answers to John’s correct answers?
Solution:

Question 17.
The number 8,000 is first increased by 20% and then decreased by 20%. Find the resulting number.
Solution:

Question 18.
The number 12,000 is first decreased by 25% and then increased by 25%. Find the resulting number.
Solution:

Question 19.
The cost of an article is first increased by 20% and then decreased by 30%, find the percentage change in the cost of the article.
Solution:

Question 20.
The cost of an article is first decreased by 25% and then further decreased by 40%. Find the percentage change in the cost of the article.
Solution:

Percent and Percentage Exercise 7B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A man bought a certain number of oranges ; out of which 13 percent were found rotten. He gave 75% of the remaining in charity and still has 522 oranges left. Find how many had he bought?
Solution:

Question 2.
5% pupil in a town died due to some diseases and 3% of the remaining left the town. If 2, 76, 450 pupil are still in the town; find the original number of pupil in the town.
Solution:

Question 3.
In a combined test in English and Physics; 36% candidates failed in English; 28% failed in Physics and 12% in both; find:
(i) the percentage of passed candidates
(ii) the total number of candidates appeared, if 208 candidates have failed.
Solution:

Question 4.
In a combined test in Maths and Chemistry; 84% candidates passsed in Maths; 76% in Chemistry and 8% failed in both. Find :
(i) the percentage of failed candidates ;
(ii) if 340 candidates passed in the test ; then how many appeared?
Solution:

Question 5.
A’s income is 25% more than B’s. Find, B’s income is how much percent less than A’s.
Solution:

Question 6.
Mona is 20% younger than Neetu. How much percent is Neetu older than Mona?
Solution:

Question 7.
If the price of sugar is increased by 25% today; by what percent should it be decreased tomorrow to bring the price back to the original?
Solution:

Question 8.
A number increased by 15% becomes 391. Find the number.
Solution:

Question 9.
A number decreased by 23 % becomes 539. Find the number.
Solution:

Question 10.
Two numbers are respectively 20 percent and 50 percent more than a third number. What percent is the second of the first?
Solution:

Question 11.
Two numbers are respectively 20 percent and 50 percent of a third number. What percent is the second of the first?
Solution:

Question 12.
Two numbers are respectively 30 percent and 40 percent less than a third number. What percent is the second of the first?
Solution:

Percent and Percentage Exercise 7C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A bag contains 8 red balls, 11 blue balls and 6 green balls. Find the percentage of blue balls in the bag.
Solution:

Question 2.
Mohan gets Rs. 1, 350 from Geeta and Rs. 650 from Rohit. Out of the total money that Mohan gets from Geeta and Rohit. what percent does he get from Rohit?
Solution:

Question 3.
The monthly income of a man is Rs. 16, 000. 15 percent of it is paid as income-tax and 75% of the remainder is spent on rent, food, clothing, etc. How much money is still left with the man?
Solution:

Question 4.
A number is first increased by 20% and the resulting number is then decreased by 10%. Find the overall change in the number as percent.
Solution:

Question 5.
A number is increased by 10% and the resulting number is again increased by 20%. What is the overall percentage increase in the number?
Solution:

Question 6.
During 2003, the production of a factory decreased by 25%. But, during 2004, it (production) increased by 40% of what it was at the beginning of2004. Calculate the resulting change (increase or decrease) in production during these two years.
Solution:

Question 7.
Last year, oranges were available at Rs. 24 per dozen ; but this year, they are available at Rs. 50 per score. Find the percentage change in the price of oranges.
Solution:

Question 8.
In an examination, Kavita scored 120 out of 150 in Maths, 136 out of 200 in English and 108 out of 150 in Science. Find her percentage score in each subject and also on the whole (aggregate).
Solution:

Question 9.
A is 25% older than B. By what percent is B younger than A ?
Solution:

Question 10.
(i) Increase 180 by 25%.
(ii) Decrease 140 by 18%.
Solution:

Question 11.
In an election, three candidates contested and secured 29200, 58800 and 72000 votes. Find the percentage of votes scored by winning candidate.
Solution:

Question 12.
(i) A number when increased by 23% becomes 861 ; find the number.
(ii) A number when decreased by 16% becomes 798 ; find the number.
Solution:

Question 13.
The price of sugar is increased by 20%. By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain the same?
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

Lines and Angles Exercise 14A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, true or false :
(i) A line segment 4 cm long can have only 2000 points in it.
(ii) A ray has one end point and a line segment has two end-points.
(iii) A line segment is the shortest distance between any two given points.
(iv) An infinite number of straight lines can be drawn through a given point.
(v) Write the number of end points in
(a) a line segment AB (b) arayAB
(c) a lineAB
(vi) Out of \(\overleftrightarrow { AB }\) , \(\overrightarrow { AB }\) , \(\overleftarrow { AB }\) and \(\overline { AB }\) , which one has a fixed length?
(vii) How many rays can be drawn through a fixed point O?
(viii) How many lines can be drawn through three
(a) collinear points?
(b) non-collinear points?
(ix) Is 40° the complement of 60°?
(x) Is 45° the supplement of 45°?
Solution:

Question 2.
In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Give, in each case, reason for your answer.

Solution:

Question 3.
In the given figure, B AC is a straight line.
Find : (i) x (ii) ∠AOB (iii) ∠BOC

Solution:

Question 4.
Find yin the given figure.

Solution:

Question 5.
In the given figure, find ∠PQR.

Solution:

Question 6.
In the given figure. p° = q° = r°, find each.

Solution:

Question 7.
In the given figure, if x = 2y, find x and y

Solution:

Question 8.
In the adjoining figure, if b° = a° + c°, find b.

Solution:

Question 9.
In the given figure, AB is perpendicular to BC at B.
Find : (i) the value of x.
(ii) the complement of angle x.

Solution:

Question 10.
Write the complement of:


Solution:

Question 11.
Write the supplement of:
(i) 100°
(ii) 0°
(iii) x°
(iv) (x + 35)°
(v) (90 +a + b)° f
(vi) (110 – x – 2y)°
(vii) \(\frac { 1 }{ 5 }\) of a right angle
(viii) 80° 49′ 25″
Solution:

Question 12.
Are the following pairs of angles complementary ?
(i) 10° and 80°
(ii) 37° 28′ and 52° 33′
(iii) (x+ 16)°and(74-x)°
(iv) 54° and \(\frac { 2 }{ 5 }\) of a right angle.
Solution:

Question 13.
Are the following pairs of angles supplementary?

Solution:

Question 14.
If 3x + 18° and 2x + 25° are supplementary, find the value of x.
Solution:

Question 15.
If two complementary angles are in the ratio 1:5, find them.
Solution:

Question 16.
If two supplementary’ angles are in the ratio 2 : 7, find them.
Solution:

Question 17.
Three angles which add upto 180° are in the ratio 2:3:7. Find them.
Solution:

Question 18.
20% of an angle is the supplement of 60°. Find the angle.
Solution:

Question 19.
10% of x° is the complement of 40% of 2x°. Find x
Solution:

Question 20.
Use the adjacent figure, to find angle x and its supplement.

Solution:

Question 21.
Find k in each of the given figures.

Solution:

Question 22.
In the given figure, lines PQ, MN and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.

Solution:

Question 23.
In the given figure, find ∠AOB and ∠BOC.

Solution:

Question 24.
Find each angle shown in the diagram.

Solution:

Question 25.
AB, CD and EF are three lines intersecting at the same point.
(i) Find x, if y = 45° and z = 90°.
(ii) Find a, if x = 3a, y = 5x and r = 6x.

Solution:

Lines and Angles Exercise 14B – Selina Concise Mathematics Class 7 ICSE Solutions

In questions 1 and 2, given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles :
Question 1.
(i) ∠3 and ∠6
(ii) ∠2 and ∠4
(iii) ∠3 and ∠7
(iv) ∠2 and ∠7
(v) ∠4 and∠6
(vi) ∠1 and ∠8
(vii) ∠1 and ∠5
(viii) ∠1 and ∠4
(ix) ∠5 and ∠7

Solution:

Question 2.
(i) ∠1 and ∠4
(ii) ∠4 and ∠7
(iii) ∠10 and ∠12
(iv) ∠7 and ∠13
(v) ∠6 and ∠8
(vi) ∠11 and ∠8
(vii) ∠7 and ∠9
(viii) ∠4 and ∠5
(ix) ∠4 and ∠6
(x) ∠6 and ∠7
(xi) ∠2 and ∠13

Solution:

Question 3.
In the given figures, the arrows indicate parallel lines. State which angles are equal. Give reasons.

Solution:

Question 4.
In the given figure, find the measure of the unknown angles :

Solution:

Question 5.
Which pair of the dotted line, segments, in the following figures, are parallel. Give reason:


Solution:

Question 6.
In the given figures, the directed lines are parallel to each other. Find the unknown angles.



Solution:







>

Question 7.
Find x. y and p is the given figures

Solution:

Question 8.
Find x in the following cases :



Solution:

Lines and Angles Exercise 14C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Using ruler and compasses, construct the following angles :
(i)30°
(ii)15°
(iii) 75°
(iv) 180°
(v) 165°
(vi) 22.5°
(vii) 37.5°
(viii) 67.5°
Solution:

Question 2.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses only. Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.
Solution:

Question 3.
Draw a line segment PQ = 6 cm. Mark a point A in PQ so that AP = 2 cm. At point A, construct angle QAR = 60°.
Solution:

Question 4.
Draw a line segment AB = 8 cm. Mark a point P in AB so that AP = 5 cm. At P, construct angle APQ = 30°.
Solution:

Question 5.
Construct an angle of 75° and then bisect it.
Solution:

Question 6.
Draw a line segment of length 6 .4 cm. Draw its perpendicular bisector.
Solution:

Question 7.
Draw a line segment AB = 5.8 cm. Mark a point P in AB such that PB = 3.6 cm. At P, draw perpendicular to AB.
Solution:

Question 8.
In each case, given below, draw a line through point P and parallel to AB :

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets

Sets Exercise 6A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Write the following sets in roster (Tabular) form :
(i) A₁ = {x : 2x + 3 = 11}
(ii) A₂ = {x : x² – 4x – 5 = 0}
(iii) A₃ = {x : x ∈ Z, -3 ≤ x < 4}
(iv) A₄ = {x : x is a two digit number and sum of digits of x is 7}
(v) A₅ = {x : x = 4n, n ∈ W and n < 4}
(vi) A₆ = {x : x = \(\frac{n}{n+2}\); n ∈ N and n > 5}
Solution:

Question 2.
Write the following sets in set-builder (Rule Method) form :

Solution:

Question 3.
(i) Is {1, 2, 4, 16, 64} = {x : x is a factor of 32} ? Give reason.
(ii) Is {x : x is a factor of 27} ≠ {3, 9, 27, 54} ? Give reason.
(iii) Write the set of even factors of 124.
(iv) Write the set of odd factors of 72.
(v) Write the set of prime factors of 3234.
(vi) Is {x : x² – 7x + 12 = 0} = {3, 4} ?
(vii) Is {x : x² – 5x – 6 = 0} = {2, 3} ?
Solution:

Question 4.
Write the following sets in Roster form :
(i) The set of letters in the word ‘MEERUT’.
(ii) The set of letters in the word ‘UNIVERSAL’.
(iii) A = {x : x = y + 3, y ∈N and y > 3}
(iv) B = {p : p ∈ W and p² < 20}
(v) C = {x : x is composite number and 5 < x < 21}
Solution:

Question 5.
List the elements of the following sets :
(i) {x : x² – 2x – 3 = 0}
(ii) {x : x = 2y + 5; y ∈ N and 2 ≤ y < 6}
(iii) {x : x is a factor of 24}
(iv) {x : x ∈ Z and x² ≤ 4}
(v) {x : 3x – 2 ≤ 10, x ∈ N}
(vi) {x : 4 – 2x > -6, x ∈ Z}
Solution:

Sets Exercise 6B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the cardinal number of the following sets :
(i) A₁ = {-2, -1, 1, 3, 5}
(ii) A₂ = {x : x ∈ N and 3 ≤ x < 7}
(iii) A₃ = {p : p ∈ W and 2p – 3 < 8}
(iv) A₄ = {b : b ∈ Z and -7 < 3b – 1 ≤ 2}
Cardinal Number of a set; The number of elements in a set is called is Cardinal Number.
Solution:

Question 2.
If P = {P : P is a letter in the word “PERMANENT”}. Find n (P).
Solution:

Question 3.
State, which of the following sets are finite and which are infinite :

Solution:

Question 4.
Find, which of the following sets are singleton sets :
(i) The set of points of intersection of two non-parallel st. lines in the same plane
(ii) A = {x : 7x – 3 = 11}
(iii) B = {y : 2y + 1 < 3 and y ∈ W}
Note : A set, which has only one element in it, is called a SINGLETON or unit set.
Solution:

Question 5.
Find, which of the following sets are empty :
(i) The set of points of intersection of two parallel lines.
(ii) A = {x : x ∈ N and 5 < x < 6}
(iii) B = {x : x² + 4 = 0, x ∈ N}
(iv) C = {even numbers between 6 & 10}
(v) D = {prime numbers between 7 & 11}
Note : The set, which has no element in it, is called the empty or null set.
Solution:

Question 6.
(i) Are the sets A = {4, 5, 6} and B = {x : x² – 5x – 6 = 0} disjoint ?
(ii) Are the sets A = {b, c, d, e} and B = {x : x is a letter in the word ‘MASTER’} joint ?
Note :
(i) Two sets are said to be joint sets, if they have atleast one element in common.
(ii) Two sets are said to be disjoint, if they have no element in common.
Solution:

Question 7.
State, whether the following pairs of sets are equivalent or not :
(i) A = {x : x ∈ N and 11 ≥ 2x – 1} and B = {y : y ∈ W and 3 ≤ y ≤ 9}
(ii) Set of integers and set of natural numbers.
(iii) Set of whole numbers and set of multiples of 3.
(iv) P = {5, 6, 7, 8} and M = {x : x ∈ W and x < 4}
Note : Two sets are said to be equivalent, if they contain the same number of elements.
Solution:

Question 8.
State, whether the following pairs of sets are equal or not :
(i) A = {2, 4, 6, 8} and
B = {2n : n ∈ N and n < 5}
(ii) M = {x : x ∈ W and x + 3 < 8} and
N = {y : y = 2n – 1, n ∈ N and n < 5}
(iii) E – {x : x² + 8x – 9 = 0} and
F = {1, -9}
(iv) A = {x : x ∈ n, x < 3} and
B = {y : y² – 3y + 2 = 0}
Note: Two sets are equal, if both the sets have same (identical) elements.
Solution:

Question 9.
State whether each of the following sets is a finite set or an infinite set:
(i) The set of multiples of 8.
(ii) The set of integers less than 10.
(iii) The set of whole numbers less than 12.
(iv) {x : x = 3n – 2, n ∈ W, n ≤ 8}
(v) {x : x = 3n – 2,n ∈ Z, n ≤ 8}
(vi) {x : x = \(\frac { n-2 }{ n+1 }\) , n ∈ w)
Solution:

Question 10.
Answer, whether the following statements are true or false. Give reasons.
(i) The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets.
(ii) If E = {factors of 16} and F = {factors of 20}, then E = F.
(iii) The set A = {integers less than 20} is a finite set.
(iv) If A = {x : x is an even prime number}, then set A is empty.
(v) The set of odd prime numbers is the empty set.
(vi) The set of squares of integers and the set of whole numbers are equal sets.
(vii) In n(P) = n(M), then P → M.
(viii) If set P = set M, then n(P) = n(M).
(ix) n(A) = n(B) ⇒ A = B.
Solution:

Sets Exercise 6C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find all the subsets of each of the following sets :
(i) A = {5, 7}
(ii) B = {a, b, c}
(iii) C = {x : x ∈ W, x ≤ 2}
(iv) {p : p is a letter in the word ‘poor’}
Solution:

Question 2.
If C is the set of letters in the word “cooler”, find :
(i) Set C
(ii) n(C)
(iii) Number of its subsets
(iv) Number of its proper subsets.
Note : (i) If a set has n elements, the number of its subsets = 2ⁿ
(ii) If a set has n elements, the number of its proper subsets = 2ⁿ – 1
Solution:

Question 3.
If T = {x : x is a letter in the word ‘TEETH’}, find all its subsets.
Solution:

Question 4.
Given the universal set = {-7,-3, -1, 0, 5, 6, 8, 9}, find :
(i) A = {x : x < 2}
(ii) B = {x : -4 < x < 6}
Solution:

Question 5.
Given the universal set = {x : x ∈ N and x < 20}, find :
(i) A = {x : x = 3p ; p ∈ N}
(ii) B = {y : y – 2n + 3, n ∈ N}
(iii) C = {x : x is divisible by 4}
Solution:

Question 6.
Find the proper subsets of {x : x² – 9x – 10 = 0}
Solution:

Question 7.
Given, A = {Triangles}, B = {Isosceles triangles}, C = {Equilateral triangles}. State whether the following are true or false. Give reasons.
(i) A ⊆ B
(ii) B ⊆ A
(iii) C ⊆  B
(iv) B ⊂ A
(v) C ⊂ A
(vi) C ⊆  B ⊆  A
Solution:

Question 8.
Given, A = {Quadrilaterals}, B = {Rectangles}, C = {Squares}, D= {Rhombuses}. State, giving reasons, whether the following are true or false.
(i) B ⊂ C
(ii) D ⊂ B
(iii) C ⊆ B ⊆ A
(iv) D ⊂ A
(v) B ⊇ C
(vi) A ⊇ B ⊇ D
Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Sets Exercise 6D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.


Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Sets Exercise 6E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.
From the given diagram, find :
(i) A’
(ii) B’

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.


Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 5 Playing with Number

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 5 Playing with Number

Playing with Number Exercise 5A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Write the quotient when the sum of 73 and 37 is divided by
(i) 11
(ii) 10
Solution:

Question 2.
Write the quotient when the sum of 94 and 49 is divided by
(i) 11
(ii) 13
Solution:

Question 3.
Find the quotient when 73 – 37 is divided by
(i) 9
(ii) 4
Solution:

Question 4.
Find the quotient when 94 – 49 is divided by
(i) 9
(ii) 5
Solution:

Question 5.
Show that 527 + 752 + 275 is exactly divisible by 14.
Solution:

Question 6.
If a = 6, show that abc = bac.
Solution:

Question 7.
If a > c; show that abc – cba = 99(a – c).
Solution:

Question 8.
If c > a; show that cba – abc = 99(c – a).
Solution:

Question 9.
If a = c, show that cba – abc = 0.
Solution:

Question 10.
Show that 954 – 459 is exactly divisible by 99.
Solution:

Playing with Number Exercise 5B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Playing with Number Exercise 5C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find which of the following nutpbers are divisible by 2:
(i) 192
(ii) 1660
(iii) 1101
(iv) 2079
Solution:

Question 2.
Find which of the following numbers are divisible by 3:
(i) 261
(ii) 111
(iii) 6657
(iv) 2574
Solution:

Question 3.
Find which of the following numbers are divisible by 4:
(i) 360
(ii) 3180
(iii) 5348
(iv) 7756
Solution:

Question 4.
Find which of the following numbers are divisible by 5 :
(i) 3250
(ii) 5557
(iii) 39255
(iv) 8204
Solution:

Question 5.
Find which of the following numbers are divisible by 10:
(i) 5100
(ii) 4612
(iii) 3400
(iv) 8399
Solution:

Question 6.
Which of the following numbers are divisible by 11 :
(i) 2563
(ii) 8307
(iii) 95635
Solution:

Playing with Number Exercise 5D – Selina Concise Mathematics Class 8 ICSE Solutions

For what value of digit x, is :
Question 1.
1×5 divisible by 3?
Solution:

Question 2.
31×5 divisible by 3?
Solution:

Question 3.
28×6 a multiple of 3?
Solution:

Question 4.
24x divisible by 6 ?
Solution:

Question 5.
3×26 a multiple of 6?
Solution:

Question 6.
42×8 divisible by 4?
Solution:

Question 7.
9142x a multiple of 4?
Solution:

Question 8.
7×34 divisible by 9?
Solution:

Question 9.
5×555 a multiple of 9 ?
Solution:

Question 10.
3×2 divisible by 11?
Solution:

Question 11.
5×2 a multiple of 11?
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Profit, Loss and Discount Exercise 8A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Megha bought 10 note-books for Rs.40 and sold them at Rs.4.75 per note-book. Find, her gain percent.
Solution:

Question 2.
A fruit-seller buys oranges at 4 for Rs.3 and sells them at 3 for Rs.4 Find his profit percent.
Solution:

Question 3.
A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs.108. Find ;
(i) his gain as percent;
(ii) the number of articles sold to make a profit of Rs.75.
Solution:

Question 4.
A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycles for Rs. 207. Find his gain or loss percent.
Solution:

Question 5.
An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportations, etc. ; find he loss or the gain as percent.
Solution:

Question 6.
Mohit sold a T.V. for Rs. 3,600 ; gaining one-sixth of its selling price. Find :
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.
Solution:

Question 7.
By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find :
(i) the loss incured
(ii) the cost price of the goods
(iii) the loss as percent.
Solution:

Question 8.
The selling price of a sofa-set is \(\frac { 4 }{ 5 }\) times of its cost price. Find the gain or the loss as percent.
Solution:

Question 9.
The cost price of an article is \(\frac { 4 }{ 5 }\) times of its selling price. Find the loss or the gain as percent.
Solution:

Question 10.
A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?
Solution:

Question 11.
The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Solution:

Question 12.
The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.
Solution:

Question 13.
A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.
Solution:

Question 14.
A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :
(i) its cc price;
(ii) the loss percent.
Solution:

Question 15.
A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;
(i) its cost price;
(ii) the profit percent.
Solution:

Profit, Loss and Discount Exercise 8B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the selling price, if:
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution:

Question 2.
Find the cost price, if :
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution:

Question 3.
By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
Solution:

Question 4.
By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
Solution:

Question 5.
Find the selling price, if :
(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20
(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%
Solution:

Question 6.
If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5%?
Solution:

Question 7.
A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16%?
Solution:

Question 8.
By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent ; if he sells the same sofa-set for Rs.3150.
Solution:

Question 9.
Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution:

Question 10.
A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player.
(iii) the total C.P. of both.
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole
Solution:

Question 11.
Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh
Solution:

Question 12.
John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it ?
Solution:

Profit, Loss and Discount Exercise 8C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A stationer buys pens at 5 for Rs.28 and sells them at a profit of 25 %. How much should a customer pay; if he buys
(i) only one pen ;
(ii) three pens ?
Solution:

Question 2.
A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :
(i) C.P. of 4 oranges,
(ii) C.P. of one orange.
(iii) S.P. of one orange.
(iv) profit made by selling one orange.
(v) number of oranges brought and sold in order to gain Rs. 24.
Solution:

Question 3.
A man sells 12 articles for Rs. 80 gaining 33\(\frac { 1 }{ 3 }\) %. Find the number of articles bought by the man for Rs. 90.
Solution:

Question 4.
The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
Solution:

Question 5.
The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
Solution:

Question 6.
By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
Solution:

Question 7.
A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
If he desires a profit of 12% on the whole ; find :
(i) the selling price of the rest of the rice ;
(ii) the percentage profit on the rest of the rice.
Solution:

Question 8.
Mohan bought a certain number of note-books for Rs.600. He sold \(\frac { 1 }{ 4 }\) of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole ?
Solution:

Question 9.
Raju sells a watch at 5% profit. Had he sold it for Rs.24 more ; he would have gained 11%. Find the cost price of the watch.
Solution:

Question 10.
A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
Solution:

Question 11.
Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs.36 more; she would have gained 20%. Find the cost price of the article.
Solution:

Profit, Loss and Discount Exercise 8D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
An article is marked for Rs. 1,300 and is sold for Rs. 1,144 ; find the discount percent.
Solution:

Question 2.
The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution:

Question 3.
A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400 ; find the discount given and the selling price of the watch.
Solution:

Question 4.
A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution:

Question 5.
A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :
(i) the marked price of the article.
(ii) the selling price, if he sells the articles at 10 percent discount.
(iii) the percentage discount given by him, if he sells the article for Rs.496.80
Solution:

Question 6.
The list price of an article is Rs.800 and is available at a discount of 15 percent. Find :
(i) selling price of the article ;
(ii) cost price of the article, if a profit of 13\(\frac { 1 }{ 3 }\) % is made on selling it.
Solution:

Question 7.
An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution:

Question 8.
By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440 ; find :
(i) the marked price of the article.
(ii) the cost price of the article.
Solution:

Question 9.
A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
Solution:

Question 10.
A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.
Solution:

Question 11.
At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution:

Question 12.
The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.
Solution:

Question 13.
Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?
Solution:

Question 14.
The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:
(i) Its marked price
(ii) its selling price
(iii) the profit percent.
Solution:

Question 15.
Find a single discount (as percent) equivalent to following successive discounts:
(i) 20% and 12%
(ii) 10%, 20% and 20%
(iii) 20%, 10% and 5%
Solution:

Question 16.
Find the single discount (as percent) equivalent to successive discounts of:
(i) 80% and 80%
(ii) 60% and 60%
(iii) 60% and 80%
Solution:

Profit, Loss and Discount Exercise 8E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Rajat purchases a wrist-watch costing Rs. 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.
Solution:

Question 2.
Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution:

Question 3.
The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.
Solution:

Question 4.
Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution:

Question 5.
The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V. ?
Solution:

Question 6.
The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution:

Question 7.
A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution:

Question 8.
When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V. ; Mrs. Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution:

Question 9.
A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.
Solution:

Profit, Loss and Discount Exercise 8F – Selina Concise Mathematics Class 8 ICSE Solutions

[In this exercise, all the prices are excluding tax/VAT unless specified]
Question 1.
A shopkeeper buys an article for ₹ 8,000 and sells it for ₹ 10,000. If the rate of tax under VAT is 10%, find :
(i) tax paid by the shopkeeper
(ii) tax charged by the shopkeeper
(iii) VAT paid by the shopkeeper
Solution:

Question 2.
A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?
Solution:

Question 3.
The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.
Solution:

Question 4.
A buys some goods for ₹ 4,000 and sold them to B for ₹ 5,000. B sold these goods to C for ₹ 6,000. If the rate of tax (under VAT) at each stage is 5%, find :
(i) VAT paid by A
(ii) VAT paid by B
Solution:

Question 5.
A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :
(i) tax paid by A
(ii) tax charged by A
(iii) VAT paid by A
Solution:

Question 6.
A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.
Solution:

Question 7.
A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.
Solution:

Question 8.
A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.
Solution:

Question 9.
The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:
(i) distributor
(ii) trader
Solution:

Question 10.
The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions