## Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

**Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)**

### Proportion Exercise 12A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

In each of the following, check whether or not the given ratios form a proportion :

(i) 8 : 16 and 12 : 15

(ii) 16 : 28 and 24 : 42

(iii) 12 ÷ 3 and 8 ÷ 2

(iv) 25 : 40 and 20 : 32

(v) \(\frac { 15 }{ 18 } and \frac { 10 }{ 12 }\)

(vi) \(\frac { 7 }{ 8 }\) and 14 : 16

Solution:

Question 2.

Find the value of x in .each of the following proportions :

(i) x : 4 = 6 : 8

(ii) 14 : x = 7 : 9

(iii) 4 : 6 = x : 18

(iv) 8 : 10 = x : 25

(v) 5 : 15 = 4 : x

(vi) 16 : 24 = 6 : x

Solution:

Question 3.

Find the value of x so that the given four numbers are in proportion :

(i) x, 6, 10 and 15

(ii) x, 4, 15 and 30

(iii) 2, x, 10 and 25

(iv) 4, x, 6 and 18

(v) 9, 12, x and 8

(vi) 4, 10, 36 and x

(vii) 7, 21, x and 45

(viii) 6, 8, 12 and x.

Solution:

Question 4.

The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.

Solution:

Question 5.

Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.

Solution:

Question 6.

Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.

Solution:

Question 7.

The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.

Solution:

Question 8.

The ratio of the sale of eggs on a Sunday and that of the whole week at a grocery shop was 2 : 9. If the total value of the sale of eggs in the same week was Rs 360, find the value of the sale of eggs that Sunday.

Solution:

Question 9.

The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg ; find the weight of copper in the alloy.

Solution:

Question 10.

The ratio of the number of girls to the number of boys in a school is 2 : 5. If the number of boys is 225 ; find:

(i) the number of girls in the school.

(ii) the number of students in the school.

Solution:

Question 11.

In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass ?

Solution:

Question 12.

Make set of all possible proportions from the numbers 15, 18, 35 and 42.

Solution:

### Proportion Exercise 12B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

If x, y and z are in continued proportion, then which of the following is true :

(i) x : y = x : z

(ii) x : x = z : y

(iii) x : y = y : z

(iv) y : x = y : z

Solution:

Question 2.

Which of the following numbers are in continued proportion :

(i) 3, 6 and 15

(ii) 15, 45 and 48

(iii) 6, 12 and 24

(iv) 12, 18 and 27

Solution:

Question 3.

Find the mean proportion between

(i) 3 and 27

(ii) 0.06 and 0.96

Solution:

Question 4.

Find the third proportional to :

(i) 36, 18

(ii) 5.25, 7

(iii) ₹ 1.60, ₹ 0.40

Solution:

Question 5.

The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.

Solution:

Question 6.

If (4x + 3y) : (3x + 5y) = 6 : 7, find :

(i) x : y

(ii) x, if y = 10

(iii) y, if x = 27

Solution:

Question 7.

If \(\frac { 2y+5x }{ 3y-5x } =2\frac { 1 }{ 2 }\), find:

(i) x : y

(ii) x, if y = 70

(iii) y, if x = 33

Solution:

### Proportion Exercise 12C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

Are the following numbers in proportion:

(i) 32, 40, 48 and 60 ?

(ii) 12,15,18 and 20 ?

Solution:

Question 2.

Find the value of x in each of the following such that the given numbers are in proportion.

(i) 14, 42, x and 75

(ii) 45, 135, 90 and x

Solution:

Question 3.

The costs of two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800 ; find the cost of the second article.

Solution:

Question 4.

The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.

Solution:

Question 5.

The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.

Solution:

Question 6.

A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.

Solution:

Question 7.

Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?

Solution:

Question 8.

Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?

Solution:

Question 9.

10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x

Solution:

Question 10.

The length of two ropes are in the ratio 7 : 5. Find the length of:

(i) shorter rope, if the longer one is 22.5 ni

(ii) longer rope, if the shorter is 9.8 m.

Solution:

Question 11.

If 4, x and 9 are in continued proportion, find the value of x.

Solution:

Question 12.

If 25, 35 and x are in continued proportion, find the value of x.

Solution: