DAV Class 6 Maths Chapter 7 Worksheet 3 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 7 Worksheet 3 Solutions of Linear Equations offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 7 WS 3 Solutions

Solve the following equations:

Question 1.
x + 9 = 15
Answer:
x + 9 = 15
⇒ x + 9 – 9 = 15 – 9 (Subtracting 9 from both sides)
∴ x = 6

Question 2.
y – 6 = 9
Answer:
y – 6 = 9
⇒ y – 6 + 6 = 9 + 6 (Adding 6 to both sides)
∴ y = 15

Question 3.
8x = 24
Answer:
8x = 24
⇒ \(\frac{8 x}{8}=\frac{24}{8}\) (Dividing both sides by 8)
⇒ x = 3

Question 4.
\(\frac{x}{5}\) = 4
Answer:
\(\frac{x}{5}\) = 4
⇒ \(\frac{x}{5}\) × 5 = 4 × 5 5 (Multiplying both sides by 5)
⇒ x = 20

DAV Class 6 Maths Chapter 7 Worksheet 3 Solutions

Question 5.
6 – y = 9
Answer:
6 – y = 9
⇒ 6 – 6 – y = 9 – 6 (Subtracting 6 from both sides)
⇒ -y = 3
∴ y = -3 (Multiplying both sides by 1)

Question 6.
x + 4 = 1
Answer:
x + 4 = 1
⇒ x + 4 – 4 = 1 – 4 (Subtracting 4 from both sides)
∴ x = -3

Question 7.
\(\frac{p}{3}\) = -8
Answer:
\(\frac{p}{3}\) = -8
⇒ \(\frac{p}{3}\) x 3 = -8 x 3 (Multiplying both sides by 3)
⇒ p = -24

Question 8.
y – 9 = 3
Answer:
y – 9 = 3
y – 9 + 9 = 3 + 9 (Adding 9 to both sides)

Question 9.
17x = -85
Answer:
17x = -85
⇒ \(\frac{17 x}{17}=\frac{-85}{17}\) (Dividing both sides by 17)
∴ x = -5

DAV Class 6 Maths Chapter 7 Worksheet 3 Solutions

Question 10.
12x = 12
Answer:
12x = 12
⇒ \(\frac{12 x}{12}=\frac{12}{12}\) (Dividing both sides by 12)
∴ x = 1

DAV Class 6 Maths Chapter 7 Worksheet 2 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 7 Worksheet 2 Solutions of Linear Equations offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 7 WS 2 Solutions

Question 1.
Check whether the given variable can solve the equation. Write ‘Yes’ or ‘No’.

Equation Value of the Variable Yes/No
(a) 10.y = 80 y = 6
(6) 6 + 5 = 9 6 = 4
(c) p – 8 = 5 p = -13
(d) \(\frac{y}{3}\)  = -1 y = -3
(e) 32 = 12 z = 2
(f) a – 4 = 5 a = 1
(g) a + 4 = 5 a = -1
(h) 2x + 1 = 7 x = 3
(i) 2x – 1 = -9 x = 4
(o) 3x = -15 x = -5

Answer:
(a) 10y = 80, variable y = 6
Put y = 6
⇒ 10 × 6 = 80
⇒ 60 ≠ 80
y = 6 is not the required solution.

(b) 6 + 5 = 9, variable 6=4
Put 6 = 4
⇒ 4 + 5 = 9
⇒ 9 = 9
∴ 6 = 4 is the solution of the given equation.

(c) p – 8 = 5, variable p = -13
Put p = -13
⇒ -13 – 8 = 5
⇒ -21 ≠ 5
∴ p = -13 is not the solution of the given equation.

DAV Class 6 Maths Chapter 7 Worksheet 2 Solutions

(d) \(\frac{y}{3}\) = -1, variable y = -3, put y = -3.
\(\frac{-3}{3}\) = -1
∴ y = -3 is the solution of the given equation.

(e) 3z = 12, variable z = 2
Put z = 2
⇒ 3 × 2 = 12
⇒ 6 ≠ 12
∴ 2 = 2 is not the required solution.

(f) a -4 = 5, variable a = 1
Put a = 1
⇒ 1 – 4= 5
⇒ -3 ≠ 5
∴ a = 1 is not the required solution.

(g) a + 4 = 5, variable a = -1
Put a = -1
⇒ -1 + 4 = 5
⇒ 3 ≠ 5
∴ a = -1 is not the required solution.

(h) 2x + 1 = 7, variable x = 3
Put x = 3,
2 × 3 + 1 = 7
⇒ 6 + 1 = 7
⇒ 7 = 7
∴x = 3 is the required solution.

(i) 2x – 1 = -9, variable x = 4
Put x = 4, 2 × 4 – 1 = -9
⇒ 8 – 1 = -9
⇒ 7 ≠-9
∴ x = 4 is not the required solution.

(j) 3x = -15, variable x = -5
Put x = -5
⇒ 3x – 5 = -15
⇒ -15 = -15
∴ x = —5 is the required solution.

DAV Class 6 Maths Chapter 7 Worksheet 1 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 7 Worksheet 1 Solutions of Linear Equations offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 7 WS 1 Solutions

Question 1.
What are the two sides of an equation called?
Answer:
Left Hand Side (LHS) and Right Hand Side (RHS).

Question 2.
In a linear equation, what is the power of the variable?
Answer:
One.

DAV Class 6 Maths Chapter 7 Worksheet 1 Solutions

Question 3.
Encircle the linear equations in the following:
(a) p + 3 = 5
(b) 2x + 3 = 7
(c) x2 + 1 = 5
(d) \(\frac{x}{3}\) = 7
(e) x3 – 1 = 9
(f) 2x – 5 = x – 3
Answer:
(a) p + 3 = 5 is linear equation
(b) 2x + 3 = 7 is linear equation
(c) \(\frac{x}{3}\) = 7 is linear equation
(d) 2x – 5 = x – 3 is linear equation

Question 4.
Separate the LHS and RHS of the following equations.

Linear equation LHS RHS
(a) y – 3 = 9
(b) 2x + 1 = 5
(c) \(\frac{y}{3}\) = 9
(d) 5y – 1 = 9 – 2y

Answer:

Linear equation LHS RHS
(a) y – 3 = 9 y – 3 9
(b) 2x + 1 = 5 2x + 1 5
(c) \(\frac{y}{3}\) = 9 \(\frac{y}{3}\) 9
(d) 5y – 1 = 9 – 2y 5y – 1 9 – 2y

DAV Class 6 Maths Chapter 7 Worksheet 1 Solutions

Question 5.
Convert the following statements into an equation:
(a) 3 added to a number x is 5.
Answer:
3 + x = 5

(b) A number y increased by 6 is 9
Answer:
y – 6 = 9

(c) 2 subtracted from a number x is equal to 10
Answer:
x – 2 = 10

(d) Twice a number p equals to 12
Answer:
2p = 12

(e) 15 less than a number a is 7
Answer:
a – 15 = 7

(f) Two-third a number x is 5
Answer:
\(\frac{2}{3}\)x = 5

(g) Three times a number x decreased by 1 is 4
Answer:
3x – 1 = 4

(h) Six times a number y is 3 more than the number itself
Answer:
6y = y + 3

(i) 5 less than one-third a number 2 is 5
Answer:
\(\frac{z}{3}\) – 5 = 5

(j) Two times the sum of a number x and 3 equals 14.
Answer:
2(x + 3) = 14

DAV Class 6 Maths Chapter 7 Worksheet 1 Notes

An equation in which the power of the variable is one is called a Linear Equation.
Example:

  • 2x + 3 = 7
  • \(\frac{2}{3}\)y + 5 = 0
  • x – 7 = 0
  • y = 0

Equation has two sides LHS and RHS
2x + 5 = 3
2x + 5 is the term on LHS and 3 is the term on RHS

Rules for solving an equation:
1. Same quantity can be added or subtracted from both sides of equality.
Example:
(i) 2x + 5 = 3
⇒ 2x + 5 – 3 = 3 – 3
⇒ 2x + 2 = 0

(ii) 3x – 7 = 5
⇒ 3x – 7 + 7 = 5 + 7
⇒ 3x = 12

2. Both sides can be multiplied by the same quantity.
Example:
5x + 2 = \(\frac{3}{2}\)
2 × (5x + 2) = \(\frac{3}{2}\) × 2
⇒ 10x + 4 = 3

3. Both sides can be divided by the same quantity
Example:
4x + 8 = 10
⇒ \(\frac{4 x+8}{2}=\frac{10}{2}\)
⇒ 2x + 4 = 5

From the above examples we can conclude that whatever we do to one side, we should do the same to the other side also.
Example 1.
Solve 3x + 8 = 14.
Solution:
3x + 8 = 14
⇒ 3x + 8 – 8 = 14 – 8 (Subtracting 8 from both sides)
⇒ 3x = 6
⇒ \(\frac{3 x}{3}=\frac{6}{3}\) (Dividing both sides by 3)
⇒ x = 2
Hence x = 2 is the solution of the given equation.

Example 2.
Solve : \(\) = 7
Solution:
\(\) = 7
⇒ \(\) x 2 = 7 x 2 (Multiplying both sides by 2)
⇒ 2y – 4 = 14
⇒ 2y-4 + 4 = 14 + 4 (Adding 4 to both sides)
⇒ 2y = 18
⇒ \(\frac{2 y}{2}=\frac{18}{2}\) (Dividing both sides by 2)
⇒ y = 9
Hence, y = 9 is the solution of the given equation.

DAV Class 5 Maths Chapter 13 Worksheet 1 Solutions

The DAV Books Solutions Class 5 Maths and DAV Class 5 Maths Chapter 13 Worksheet 1 Solutions of Simple Interest offer comprehensive answers to textbook questions.

DAV Class 5 Maths Ch 13 Worksheet 1 Solutions

Question 1.
Fill in the blanks.
(a) The money deposited in a bank is called __________
Solution:
Principal

(b) The extra money paid by the bank is called __________
Solution:
Interest

(c) The period of time for which money is kept in a bank is called __________
Solution:
Time

DAV Class 5 Maths Chapter 13 Worksheet 1 Solutions

(d) The money borrowed from a bank is called __________
Solution:
Principal (loan)

(e) Extra money charged by the bank for every hundred rupees deposit is called __________
Solution:
Interest

DAV Class 5 Maths Chapter 13 Worksheet 1 Notes

  • Principal: Money deposited in a bank is called Principal.
  • Interest: The extra money paid by the bank is called Interest.
  • Time: The period of time after which money is withdrawn is called time.
  • Rate of Interest: The extra money paid by the bank for every ₹ 100 after one year is called the Rate of Interest.
  • The bank also gives a loan. A person has to return it within a certain time limit alongwith some interest charged by the bank.
  • Here, the money borrowed (loan) is the Principal and the extra money to be paid is called the interest.
  • The bank utilizes the money deposited in the form of loans to customers or invests in some project. The bank earns interest on the same.
  • Simple Interest = Principal × Rate of Interest × Time
  • Amount = Principal + Interest
  • Principal = Amount – Interest
  • Interest = Amount – Principal

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

The DAV Books Solutions Class 5 Maths and DAV Class 5 Maths Chapter 12 Brain Teasers Solutions of Percentage offer comprehensive answers to textbook questions.

DAV Class 5 Maths Ch 12 Brain Teasers Solutions

Question 1.
Tick (✓) the correct answer.
(a) 10% of 74.6 is-
(i) 4.6
(ii) 7.4
(iii) 7.46
(iv) 746
Solution:
\(\frac{10}{100}\) of 74.6 = \(\frac{10}{100}\) × 74.6 = 7.46
So, option (iii) is correct.

(b) 8 tenths = ______%
(i) 8
(ii) 80
(iii) 0.8
(iv) 0.08
Solution:
8 tenth = (\(\frac{8}{10}\) × 100)% = 80%
So, option (ii) is correct.

(c) 33\(\frac{1}{3}\)% of 10% of 600 litres = ______ litres.
(i) 20
(ii) 120
(iii) 200
(iv) 220
Solution:
33\(\frac{1}{3}\)% of 10% of 600 l
= \(\frac{100}{3}\)% × 10% × 600 l
= \(\frac{100}{3} \times \frac{1}{100} \times \frac{10}{100}\) × 600 l
= 20 l
So, option (i) is correct.

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

(d) The percentage of shaded part in the given figure is-
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Q1(d)
(i) 80%
(ii) 70%
(iii) 75%
(iv) 85%
Solution:
\(\frac{3}{4}\) = (\(\frac{3}{4}\) × 100)% = 75%
So, option (iii) is correct.

(e) Jack went up the hill and came down with a bucket three-fifth filled with water. Then the percentage of water left to be filled in the bucket is-
(i) 60%
(ii) 30%
(iii) 40%
(iv) 50%
Solution:
\(\frac{3}{5}\) = (\(\frac{3}{5}\) × 100)%
= (3 × 20)%
= 60%
% of water left to be filled = (100 – 60)% = 40%
So, option (iii) is correct.

Question 2.
Write each of the following as a percentage.
(a) 7 tenths
Solution:
7 tenths = (\(\frac{7}{10}\) × 100)% = 70%

(b) \(\frac{328}{100}\)
Solution:
\(\frac{328}{100}\) = (\(\frac{328}{100}\) × 100)% = 328%

(c) 0.07
Solution:
0.07 = (\(\frac{0.07}{100}\) × 100)% = 7%

(d) 5\(\frac{1}{5}\)
Solution:
5\(\frac{1}{5}\) = \(\frac{26}{5}\)
= (\(\frac{26}{5}\) × 100)%
= 520%

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

Question 3.
Express as a fraction in the lowest term.
(a) 35%
Solution:
35% = \(\frac{35}{100}\) = \(\frac{7}{20}\)

(b) 16\(\frac{2}{3}\)%
Solution:
16\(\frac{2}{3}\)% = \(\frac{50}{3 \times 100}\) = \(\frac{1}{6}\)

(c) 2\(\frac{3}{4}\)%
Solution:
2\(\frac{3}{4}\)% = \(\frac{11}{4} \times \frac{1}{100}\) = \(\frac{11}{400}\)

(d) 90%
Solution:
90% = \(\frac{90}{100}\) = \(\frac{9}{10}\)

Question 4.
Express as a decimal.
(a) 71%
Solution:
71% = \(\frac{71}{100}\) = 0.71

(b) 9.5%
Solution:
9.5% = \(\frac{9.5}{100}\) = 0.095

(c) 101%
Solution:
101% = \(\frac{101}{100}\) = 1.01

(d) 759%
Solution:
759% = \(\frac{759}{100}\) = 7.59

Question 5.
Find the value of-
(a) 33\(\frac{1}{3}\)% of 429 metres
Solution:
33\(\frac{1}{3}\)% of 429 metres
= \(\frac{100}{3 \times 100}\) × 429
= 143 m

(b) 50% of 4 metres
Solution:
50% of 4 metres
= \(\frac{50}{100}\) × 4
= 2 m

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

(c) 100% of 200 grams
Solution:
100% of 200 grams
= \(\frac{100}{100}\) × 200
= 200 gm

(d) 20% of 1 kg
Solution:
20% of 1 kg
= \(\frac{20}{100}\) × 1
= \(\frac{1}{5}\)
= 0.2 kg or 200 gms

(e) 6\(\frac{1}{4}\)% of 1 litre
Solution:
6\(\frac{1}{4}\)% of 1 litre
= \(\frac{25}{4 \times 100}\) × 1
= \(\frac{1}{16}\) l
= 0.0625 l

(f) 12\(\frac{1}{2}\)% of ₹ 32
Solution:
12\(\frac{1}{2}\)% of ₹ 32
= \(\frac{25}{2 \times 100}\) × 32
= ₹ 4

Question 6.
A school contributed ₹ 3,500 to the flood relief fund. Sonal donated 10% of the fund. How much money was donated by Sonal?
Solution:
Total contribution of school = ₹ 3,500
Sonal’s contribution = 10%
Money contribution of Sonal = \(\frac{10}{100}\) × 3500 = ₹ 350
The money donated by Sonal was ₹ 350.

Question 7.
Mr Arun earns ₹ 35,500 per month. He spends 70% on household expenses, 25% on children, and saves the rest. How much money did Arun save?
Solution:
Earning of Mr Aran per month = ₹ 35,500
His expenditure = 70% + 25% = 95%
Saves = (100 – 95)% = 5%
His savings = \(\frac{5}{100}\) × 35500 = ₹ 1,775
Arun saved ₹ 1,775.

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

Question 8.
Mr Gupta took his family out for dinner. The amount of the bill was ₹ 875. Mr Gupta paid 5% of the bill amount as a tip. Find the money given as a tip.
Solution:
Amount of bill = ₹ 875
% of tip = 5%
Money as tip = 5% of ₹ 875
Amount paid at tip = \(\frac{5}{100}\) × 875 = ₹ 43.75
The money given as tip is ₹ 43.75.

Question 9.
Find the percentage of the letter ‘M’ in the word MATHEMATICS.
Solution:
Total alphabets = 11
% of ‘M’ = (\(\frac{2}{11}\) × 100)%
= (\(\frac{200}{11}\))%
= 18\(\frac{2}{11}\)%

Question 10.
Some numbers are below:
5, 2, 18, 26, 31, 42, 65, 7, 13, 35
Find the percentage of:
(a) Even numbers
(b) Odd numbers
(c) Prime numbers
(d) Odd primes
(e) Multiples of 5
(f) Even primes
Solution:
(a) Total numbers = 10
Even numbers = 4
% of even numbers = (\(\frac{4}{10}\) × 100)% = 40%

(b) Total numbers = 10
Odd numbers = 6
% of odd numbers = (\(\frac{6}{10}\) × 100)% = 60%

(c) Total number = 10
Prime numbers = 5
% of prime numbers = (\(\frac{5}{10}\) × 100)%

(d) Total numbers = 10
Odd prime numbers = 4
% of odd primes = (\(\frac{4}{10}\) × 100)% = 40%

(e) Total numbers = 10
Multiples of 5 = 3
% of multiples of 5 = (\(\frac{3}{10}\) × 100)% = 30%

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

(f) Total numbers = 10
Even primes = 1
% of even primes = (\(\frac{1}{10}\) × 100)% = 10%

Additional Questions

Question 1.
Complete the following:
(a)
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Additional Questions Q1(a)
Solution:
\(\frac{22}{100}\) = 22%

(b)
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Additional Questions Q1(b)
Solution:
\(\frac{133}{100}\) = 133%

(c)
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Additional Questions Q1(c)
Solution:
\(\frac{46}{100}\) = 46%

(d)
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Additional Questions Q1(d)
Solution:
\(\frac{89}{100}\) = 89%

(e)
DAV Class 5 Maths Chapter 12 Brain Teasers Solutions Additional Questions Q1(e)
Solution:
\(\frac{56}{100}\) = 56%

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

Question 2.
Convert the following percentages into fractions in the lowest term:
(a) 45%
Solution:
45% = \(\frac{45}{100}\) = \(\frac{9}{20}\)

(b) 125%
Solution:
125% = \(\frac{125}{100}\)
= \(\frac{5}{4}\)
= 1\(\frac{1}{4}\)

(c) 176%
Solution:
176% = \(\frac{176}{100}\)
= \(\frac{44}{25}\)
= 1\(\frac{19}{25}\)

(d) 89%
Solution:
89% = \(\frac{89}{100}\)

Question 3.
Express the following percentages into decimals:
(a) 8.8%
Solution:
8.8% = \(\frac{8.8}{100}\) = 0.088

(b) 8.9%
Solution:
8.9% = \(\frac{8.9}{100}\) = 0.089

(c) 2.9%
Solution:
2.9% = \(\frac{2.9}{100}\) = 0.029

(d) 0.38%
Solution:
0.38% = \(\frac{0.38}{100}\) = 0.0038

Question 4.
Convert the following into percentages.
(a) \(\frac{8}{25}\)
Solution:
\(\frac{8}{25}\) = (\(\frac{8}{25}\) × 100)% = 32%

(b) 3\(\frac{1}{4}\)
Solution:
3\(\frac{1}{4}\) = (\(\frac{13}{4}\) × 100)%
= (13 × 25)%
= 325%

Question 5.
Convert the following into percentages.
(a) 0.732
Solution:
0.732 = (0.732 × 100)% = 73.2%

(b) 3.7
Solution:
3.7 = (3.7 × 100)% = 370%

(c) 31.87
Solution:
31.87 = (31.87 × 100)% = 3187%

(d) 41.35
Solution:
41.35 = (41.35 × 100)% = 4135%

DAV Class 5 Maths Chapter 12 Brain Teasers Solutions

Question 6.
Find
(a) 20% of 800
Solution:
20% of 800 = \(\frac{20}{100}\) × 800 = 160

(b) 2\(\frac{1}{4}\)% of 160
Solution:
2\(\frac{1}{4}\)% of 160 = \(\frac{9}{4}\) × \(\frac{1}{100}\) × 160 = 3.6

(c) 2% of 400
Solution:
2% of 400 = \(\frac{2}{100}\) × 400 = 8

DAV Class 6 Hindi Book Solutions Pdf – DAV Class 6 Hindi Solutions

DAV Class 6 Hindi Book Solutions Pdf: For Students who are looking for DAV Class 6 Hindi Abhyas Sagar Gyan Sagar Solutions, have a look at our article as we are going to provide you with enough Class 6 DAV Hindi Book Solution that helps to answer the question in a correct pattern using the methodology and logical approach while attending for exam.

DAV Hindi Book Solution Class 6 provides you with the worksheets to prepare for the exam and these pdf will be up to date according to the latest syllabus. Use our DAV Public School Class 6 Hindi Solutions to build a foundation with the fundamentals of the DAV Class 6 Hindi Book Pdf.

Also, Check:

DAV Public School Class 6 Hindi Book Solutions – Class 6 DAV Hindi Book Solution

Look into the list of DAV Class 6 Hindi Solution that was given below. When you want to practice, just click on the chapter you like then start preparing for exams by checking out the DAV Class 6 Hindi Question Answer that were given.

DAV Class 6 Hindi Book Solutions – Class 6 DAV Hindi Solution – DAV Books Solutions Class 6 Hindi

DAV Class 6 Hindi Gyan Sagar Solutions ज्ञान सागर

DAV Class 6 Hindi Abhyas Sagar Solutions अभ्यास सागर

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1. Which Hindi book is best for DAV class 6?

For DAV class 6 students DAV Public School Class 6 Hindi Book Pdf is more than enough. And look into our DAV Hindi Class 6 Solutions as we have given questions and answers for the same syllabus.

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You can get DAV Solution Class 6 Hindi online at our learncram.com website.

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DAV Class 5 Maths Chapter 12 Worksheet 5 Solutions

The DAV Books Solutions Class 5 Maths and DAV Class 5 Maths Chapter 12 Worksheet 5 Solutions of Percentage offer comprehensive answers to textbook questions.

DAV Class 5 Maths Ch 12 Worksheet 5 Solutions

Question 1.
Solve the following questions:
(a) Rohan gets 38 out of 50 in his monthly test of Mathematics. Express his marks in percentage.
Solution:
Maximum marks = 50
Marks scored = 38
% of marks = (\(\frac{38}{50}\) × 100)% = 76%
His mark in percentage is 76%.

(b) In a class of 45 students, 60% are boys. Find the number of boys in the category.
Solution:
Total students = 45
% of boys = 60%
No. of boys in the class = \(\frac{60}{100}\) × 45 = 27
Number of boys in the class is 27.

DAV Class 5 Maths Chapter 12 Worksheet 5 Solutions

(c) In an orchard of 400 trees, 35% are mango trees. 42% were apple trees and the rest were grape vines. How many grape vines are there?
Solution:
Total trees = 400
% of mango trees = 35%
% of apple trees = 42%
% of grape vines = (100 – 35 + 42)%
= (100 – 77)%
= 23%
Number of grape vines = 23% of 400
= \(\frac{23}{100}\) × 400
= 92
92 grape vines are there.

(d) Mr Mahesh earns ₹ 7,200 per month. He spends 33\(\frac{1}{3}\)% on food. Find the amount spent on food.
Solution:
Total earnings = ₹ 7,200 per month
Spends on food = 33\(\frac{1}{3}\)%
Amount spends on food = 33\(\frac{1}{3}\)% of ₹ 7,200
= \(\frac{100}{300}\) × 7,200
= ₹ 2,400
₹ 2,400 is spent on food.

(e) Anil got 440 marks out of 800 and Gopi got 486 marks out of 900 in an examination. Who scored better?
Solution:
Maximum marks = 800
Anil scored = 440
% of marks = (\(\frac{440}{800}\) × 100)% = 55%
Maximum marks = 900
Gopi scored = 486
% of marks = (\(\frac{486}{900}\) × 100)% = 54%
Anil scored better.

DAV Class 5 Maths Chapter 12 Worksheet 5 Solutions

DAV Class 5 Maths Chapter 12 Value Based Questions

Question 1.
What is the number of Muslims in the village?
Solution:
Total population = 3,00,000
% of Hindus = 45%
% of Sikhs = 20%
% of Muslims = [100 – (45 + 20)]%
= (100 – 65)%
= 35%
No. of Muslims = 35% of 3,00,000
= \(\frac{35}{100}\) × 3,00,000
= 35 × 3,000
= 1,05,000
The number of Muslims in the village is 1,05,000.

Question 2.
Name the festivals you celebrate together with your neighbours?
Solution:
Holi, Diwali, Dusshera, Christmas, and Id.

Word Problems

Example 1.
A man purchased 30 eggs. 10% of eggs were found to be broken. How many eggs were broken?
Solution:
Number of eggs = 30
Broken eggs = 10% of 3 eggs
= \(\frac{10}{100}\) × 30
= 3 eggs
3 eggs were broken.

DAV Class 5 Maths Chapter 12 Worksheet 5 Solutions

Example 2.
In an examination, Sunil scored 18 marks out of 25 effects. What is the percentage of marks scored by him?
Solution:
Maximum marks = 25
Marks scored = 18
% of marks = (\(\frac{18}{25}\) × 100)%
= \(\frac{1800}{25}\)%
= 72%
He scored 72%.

DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions

The DAV Books Solutions Class 5 Maths and DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions of Percentage offer comprehensive answers to textbook questions.

DAV Class 5 Maths Ch 12 Worksheet 4 Solutions

Question 1.
Find the value of the following:
(a) 50% of 10
Solution:
50% of 10 = \(\frac{50}{100}\)% of 10
= \(\frac{50}{100}\) × 10
= 5

(b) 60% of 700
Solution:
60% of 700 = \(\frac{60}{100}\)% of 700
= \(\frac{60}{100}\) × 700
= 420

(c) 24% of 75
Solution:
24% of 75 = \(\frac{24}{100}\)% of 75
= \(\frac{24}{100}\) × 75
= 18

DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions

(d) 6\(\frac{1}{4}\)% of 800
Solution:
6\(\frac{1}{4}\)% of 800 = \(\frac{25}{4}\)% of 800
= \(\frac{25}{4 \times 100}\) × 800
= 50

(e) 16\(\frac{2}{3}\)% of 1200
Solution:
16\(\frac{2}{3}\)% of 1200 = \(\frac{50}{3}\)% of 1200
= \(\frac{50}{300}\) × 1200
= 200

(f) 33\(\frac{1}{3}\)% of 300
Solution:
33\(\frac{1}{3}\) % of 300 = \(\frac{100}{3}\)% of 300
= \(\frac{100}{3 \times 100}\) × 300
= 100

(g) 75% of 300
Solution:
75% of 300 = \(\frac{75}{100}\)% of 300
= \(\frac{75}{100}\) × 300
= 225

(h) 3\(\frac{3}{4}\)% of 80
Solution:
3\(\frac{3}{4}\)% of 80 = \(\frac{15}{4}\)% of 80
= \(\frac{15}{4 \times 100}\) × 80
= 3

Question 2.
Find the value of the following:
(a) 3% of ₹ 600
Solution:
3% of ₹ 600 = \(\frac{3}{100}\) of ₹ 600
= \(\frac{3}{100}\) × 600
= ₹ 18

DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions

(b) 1% of 100 kg
Solution:
1% of 100 kg = \(\frac{1}{100}\) of 100 kg
= \(\frac{1}{100}\) × 100
= 1 kg

(c) 20% of 5 kilometres
Solution:
20% of 5 kilometres = \(\frac{20}{100}\) of 5 km
= \(\frac{20}{100}\) × 5
= 1 km

(d) 90% of 500 marks
Solution:
90% of 500 marks = \(\frac{90}{100}\) of 500 marks
= \(\frac{90}{100}\) × 500
= 450 marks

(e) 150% of 20 litres
Solution:
150% of 20 litres = \(\frac{150}{100}\) of 20 l
= \(\frac{150}{100}\) × 20
= 30 l

(f) 8% of 200 grams
Solution:
8% of 200 grams = \(\frac{8}{100}\) of 200 gm
= \(\frac{8}{100}\) × 200
= 16 gm

(g) 12\(\frac{1}{2}\)% of 1 kilogram
Solution:
12\(\frac{1}{2}\)% of 1 kilogram = \(\frac{25}{2}\)% of 1 kg
= \(\frac{25}{200}\) × 1
= \(\frac{1 \times 1}{8}\)
= 0.125 kg or 125 gm

DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions

(h) \(\frac{3}{4}\)% of ₹ 8,800
Solution:
\(\frac{3}{4}\)% of ₹ 8,800 = \(\frac{3}{400}\) of ₹ 8,800
= \(\frac{3}{400}\) × 8800
= ₹ 66

Question 3.
Find which is more of the two:
(a) 15% of 200 or 20% of 100
Solution:
15% of 200 or 20% of 100
15% of 200 = \(\frac{15}{100}\) × 200 = 30
20% of 100 = \(\frac{20}{100}\) × 100 = 20
30 > 20
Thus, 15% of 200 > 20% of 100

(b) 34% of 250 or 18% of 150
Solution:
34% of 250 or 18% of 150
34% of 250 = \(\frac{34}{100}\) × 250 = 85
18% of 150 = \(\frac{18}{100}\) × 150 = 27
85 > 27
Thus, 34% of 250 > 18% of 150

Word Problems

Example 1.
Find 20% of 50.
Solution:
20% of 50 = \(\frac{20}{100}\) × 50
= \(\frac{20 \times 50}{100}\)
= \(\frac{1000}{100}\)
= 10

DAV Class 5 Maths Chapter 12 Worksheet 4 Solutions

Example 2.
Find 33\(\frac{1}{3}\)% of 1,800 kg.
Solution:
33\(\frac{1}{3}\)% of 1,800 = \(\frac{100}{3}\)% of 1,800
= \(\frac{100}{3 \times 100}\) × 1800
= \(\frac{1800}{3}\)
= 600

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 8 Brain Teasers Solutions of Basic Geometrical Concepts offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 8 Brain Teasers Solutions

Question 1.
A. Tick (✓) the correct answer.
(a) A ________ extends endlessly in all directions.
(i) line
(ii) ray
(iii) plane
(iv) line segments
Answer:
(iii) plane

(b) Which of the following is different from others?
(i) ball
(ii) orange
(iii) globe
(iv) sticker
Answer:
(iv) sticker

(c) Three or more lines passing through the same point are called
(i) concurrent lines
(ii) intersecting lines
(iii) parallel lines
(iv) perpendicular lines
Answer:
(i) concurrent lines

(d) The opposite side(s) of a classroom blackboard represent ________ line segments.
(i) vertical
(ii) parallel
(iii) intersecting
(iv) concurrent
Answer:
(ii) parallel

(e) ________ line can pass through one given point.
(i) only one
(ii) only two
(iii) only three
(iv) many
Answer:
(iv) many.

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

B. Answer the following questions.
(a) Give two examples of objects having curved surface.
Answer:
Ball, globe.

(b) Four points A, B, C, D line on the same line l. What are these points called?
Answer:
Collinear points.

(c) Can you draw a line on the surface of a sphere, completely lying on it?
Answer:
No

(d) Give one example each of parallel and intersecting line segments from your environment.
Answer:
Lines of copy; adjacent sides of black-board.

(e) If two lines m and n cut at a point X, what is the point X called?
Answer:
Point of intersection.

Question 2.
You are given some points here. Name all the sets of collinear points.
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 1
Answer:
P, R, S and Q, S, T are the two sets of collinear points.

Question 3.
In the figure given here, name:
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 2
(a) all the pairs of parallel lines.
(b) 4 pairs of intersecting lines.
(c) the lines whose point of intersection is A.
(d) the lines whose point of inter section is D.
(e) 3 sets of collinear points.
(f) point of intersection of lines:
(i) p and r
(ii) l and p
Answer:
(a) l ∥ m ∥ n
(b) p and r, p and m, p and Z, l and r
(c) q and l
(d) l and r
(e) (A, B, C), (D, E, F) and (H, I, J)
(f) (i) J
(ii) H

Question 4.
With the help of a figure, find the maximum and the minimum number of points of intersection of four lines in a plane.
Answer:
In figure (i) A, B, C, D and E are the maximum number of points of intersection of 4 lines l, m, n and p.
∴ Total number of points is 4.
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 3
In figure (ii) s, t, u are the minimum number of points of intersection of 4 lines 1, iii., n and p.
∴ The total number of points is 3.

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

Question 5.
Write ‘True’ or ‘False’ for the following statements:
(a) Two lines in a plane always intersect at a point.
Answer:
False

(b) Two different lines can be drawn passing through two given points.
Answer:
False

(c) If two lines intersect at a point p, then p is called the point of intersection of the two lines.
Answer:
True

(d) The minimum number of points of intersection of three lines is one. three lines which pass through the same point are called intersecting lines.
Answer:
False

(e) Opposite sides of a blackboard represent parallel lines.
Answer:
False

(g) A globe has a curved surface.
Answer:
True

(h) Points which lie on the same line are called non-collinear points.
Answer:
False

Question 6.
Fill in the blanks given below:
(a) The corner of a triangle represents a ________.
Answer:
Point

(b) The table top gives an idea of a ________ surface.
Answer:
Plane

(c) The ‘plus’ sign represents ________ line segments.
Answer:
Intersecting

(d) A ________ extends infinitely in all directions.
Answer:
Plane

(e) The lines of your notebook represent ________ lines.
Answer:
Parallel

DAV Class 6 Maths Chapter 8 HOTS

Question 1.
With the help of figures find the maximum number of points of intersection of four lines and five lines in a plane.
Answer:
Do it yourself.

Question 2.
Look at the figure and answer the questions.
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 4
(a) How many line segments are there in all?
(b) Name all line segments whose one end point is:
(i) E
(ii) C
Answer:
(a) 15 line segments.
(i) EA, EB, EC, ED, EF
(ii) CA, CB, CD, CE, CF

DAV Class 6 Maths Chapter 8 Enrichment Questions

Question 1.
Look at the figure and answer the questions.
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 5
(а) How many pairs of parallel lines are there?
Answer:
5 pairs

(b) Name one set of four concurrent lines.
Answer:
AE, ID, GB, HC

(c) Name the lines whose point of intersection is:
(i) A
(ii) H
Answer:
(i) AB, AE
(ii) IG, HC

(d) Name the point of intersection of lines:
(i) ED and AE
(ii) IG and BG
Answer:
(i) E
(ii) G

(e) Name two sets of three collinear points.
Answer:
(I, G, H), (H, F, C)

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

Additional Questions

Question 1.
Classify the following figures as lines, rays and line segments.
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 6
Answer:
line

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 7
Answer:
ray

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 8
Answer:
line

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 9
Answer:
ray

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 10
Answer:
line segments

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 11
Answer:
line

Question 2.
In the given figure state:
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 12
(a) How many lines do you observe in the given figure?
(b) Name the parallel lines.
(c) Name the two sets of collinear points.
(d) Name all the intersecting lines.
(e) Name all the points of intersection.
Answer:
(a) l, m, n and p represent the lines
(b) l ∥ m
(c) (C, D, E) and (C, A, B)
(d) l, m, p and n
(e) C, A, B, D and E

Question 3.
In the given figures, Name the points and line segments:
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 13
Answer:
Points are: A, B, C, D and E
Line segments: AB, BC, CD, DA, DB, AC, ED, EA, EB and EC.

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 14
Answer:
Points are: A, B, C, D, E, F and O
Line segments: AB, BC, CD, DE, EF, FA, AD, BE, CF, OA, OB, OC, OD, OE and OF.

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 15
Answer:
Points are: A, B, C, D, E, F, G, O
Line segments: AB, BC, CD, DE, EF, FA, OA, OC, OE, BG, AF, CD, GD, FG.

Question 4.
In the given figure, find:
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 16
(a) Number and name of lines.
(b) Sets of collinear points.
(c) Point of intersection of lines m and q.
(d) If l ∥ m ∥ n
(e) If \(\overline{\mathrm{AB}}=\overline{\mathrm{BC}}\), then is it true for DE and EF?
Answer:
(a) lines, l, m, n, p and q are the names of the 5 lines.
(b) (A, B, C) and (D, E, F)
(c) E
(d) Yes l ∥ m ∥ n
(e) Yes, it is true that DE = EF

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

Question 5.
Fill in the blanks:
(a) Number of lines that can be drawn through two points is ________.
Answer:
One

(b) ________ lines can be drawn through a point.
Answer:
Infinite

(c) Two intersecting lines have one ________ point.
Answer:
Common

(d) Parallel lines do not have ________ point.
Answer:
Common

(e) Plane surface can be extended ________ is all directions.
Answer:
Endlessly

(f) The lines intersecting at one point are called ________.
Answer:
Concurrent

(g) A black board has ________ surface.
Answer:
Plane

(h) The points which lie on the same line are called ________.
Answer:
Collinear

Question 6.
Give two examples each of such letters of English alphabet having:
(a) Parallel lines
(b) Intersecting lines
Answer:
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 17

Question 7.
Give three examples each of the objects having:
(a) Flat surface
(b) Curved surface
Answer:
(a) Black board, 100-rupee note, plane paper
(b) Ball, Orange, Egg

Question 8.
Lines p, q and r are concurrent. Also lines r, s and t are concurrent. Is it always true that the lines p, q and s will be concurrent? Is it also true for the lines p, q and f!
DAV Class 6 Maths Chapter 8 Brain Teasers Solutions 18
Answer:
(i) Yes, p, q and s will be concurrent.
(ii) Yes, it is true that p, q and t are also concurrent.

Question 9.
Can you draw a line on the surface of a sphere which lies wholly on it?
Answer:
As the surface of the sphere is not plane.
So, we cannot draw any line on it.

DAV Class 6 Maths Chapter 8 Brain Teasers Solutions

Question 10.
Give two examples from your environment of:
(a) Intersecting lines
Answer:
(i) Crossing of roads
(ii) Branches of tree

(b) Parallel lines
Answer:
(i) Railway lines
(ii) Opposite sides of black board

DAV Class 6 Maths Chapter 8 Worksheet 1 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 8 Worksheet 1 Solutions of Basic Geometrical Concepts offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 8 WS 1 Solutions

Question 1.
Mark a point in your notebook and draw a line passing through it. How many lines can you draw passing through this point?
Answer:
Steps:
(i) Take any point 0.
(ii) Draw a straight line through 0 making arrow on both ends.
(iii) Name the line \(\overrightarrow{\mathrm{PQ}}\).
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 1
Infinite number of lines can be drawn through this point.

Question 2.
Mark any two points in your notebook and draw a line passing through both the points. How many such lines can you draw passing through these two given points?
Answer:
Steps:
(i) Take any two points A and B.
(ii) Put a scale at A and B and draw a line through A and B.
(iii) Extend it in both the directions making arrows on both ends.
(iv) AB is the required line.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 2
One and only one line can be drawn through two points.

Question 3.
Classify the following pairs of lines as parallel lines or intersecting lines.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 3
Answer:
Intersecting

DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 4
Answer:
Parallel

DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 5
Answer:
Parallel

DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 6
Answer:
Intersecting

DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 7
Answer:
Parallel

DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 8
Answer:
Intersecting

DAV Class 6 Maths Chapter 8 Worksheet 1 Solutions

Question 4.
Fill in the blanks:
(a) An orange has a ________ surface.
Answer:
Spherical

(b) A 100 rupee note has a ________ surface.
Answer:
Plane

(c) ________ lines can pass through one given point in a plane.
Answer:
Many

(d) Three or more points in a plane which lie on the same line are called ________.
Answer:
Collinear

(e) Lines which do not meet anywhere in a plane are called ________ lines.
Answer:
Parallel

(f) Two lines which cut each other at a point are called ________ lines.
Answer:
Concurrent

Question 5.
In the given figure write:
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 9
(a) all the pairs of parallel lines.
Answer:
l ∥ m ∥ n

(b) the lines whose point of intersection is E.
Answer:
n and r

(c) one set of 4 collinear points.
Answer:
G, F, E, D and A, B, C, D

(d) any four pairs of intersecting lines
Answer:
t and r, t and n, r and m, 1 and t

(e) the point of intersection of lines m and t.
Answer:
B

(f) the point of intersection of lines r and t.
Answer:
D

Question 6.
A, B, C are any three points in a plane. Join them in pairs. How many lines can you get if:
(a) A, B, C are collinear?
Answer:
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 10
Only one line is obtained when A, B, C are collinear.

(b) A, B, C are not collinear?
Answer:
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 11
Three fines \(\overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{BC}}\) and \(\overleftrightarrow{\mathrm{AC}}\) can be obtained if A, B, C are not collinear.

DAV Class 6 Maths Chapter 8 Worksheet 1 Solutions

Question 7.
Lines l, m and n are concurrent. Also lines r, l and m are concurrent. Draw a figure and state whether lines r, l, m and n are concurrent or not.
Answer:
Yes, the lines r, l, m and n are concurrent.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 12

Question 8.
In the given figure, name:
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 13
(a) the lines concurrent at point A.
Answer:
r, n and m

(b) all the sets of collinear points.
Answer:
(A, F, B), (B, D, C), (A, E, C)

(c) the lines concurrent at point G.
Answer:
r, q and p

(d) the point of intersection of three fines l, p and m.
Answer:
C

(e) all the points that lie in this plane.
Answer:
A, F, B, D, C, E and G

(f) two pairs of intersecting lines.
Answer:
q and n, r and p

Question 9.
In the given figure name the
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 14
(a) lines concurrent at D and B
(b) point of concurrence of fines AD, AB and AC.
Answer:
(a) Lines concurrent at D are n, l and m.
(b) Point of concurrence of fines AD, AB and AC is A.

DAV Class 6 Maths Chapter 8 Worksheet 1 Notes

Line: A straight path extendable endlessly in both the directions is called line.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 15
\(\overline{\mathrm{AB}}\) is the representation of line AB

Ray: Ray has one end point and extendable is one direction.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 16
\(\overline{\mathrm{AB}}\) represents a ray

Line segment: Line segment is a part of a line. It has two end points and definite length.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 17

Plane: Plane is a flat surface which can be extended infinitely in all directions.

Collinear points: The points which lie on the same line are called collinear points.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 18
Here P, Q, R are collinear points.

Non-collinear points:
The points which do not he on the same straight line are called non-collinear points.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 19
Here P, Q, R, S are non collinear points.

Intersecting lines: The lines which cut. each other at. a point are called intersecting lines.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 20
Here lines \(\overrightarrow{\mathrm{AB}}\) and \(\overleftrightarrow{\mathrm{CD}}\) intersect at O.
Infinite number of lines can pass through a point.

Parallel lines:
The lines which never intersect each other even on extending infinitely in both directions are calLed parallel lines.
Here \(\overleftrightarrow{\mathrm{AB}} \| \overleftrightarrow{\mathrm{CD}}\)
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 21

Concurrent lines:
The lines which pass through the same point are called concurrent lines.
Here all the lines pass through the same point O.
DAV Class 6 Maths Chapter 8 Work Sheet 1 Solutions 22