## Practice Questions – Ratio and Proportion – 1

1) The total number of students in a school is 1224. If the number of girls of students in a school is 600, then what is the respective ratio of the total number of boys to the total number of girls in the school?

a) 26 : 25

b) 21 : 17

c) 18 : 13

d) 5 : 4

e) None of these

a) 26 : 25

Explanation:

Total number of students in the school = 1224

Number of girls = 600

∴ number of boys = 1224 – 600 = 624

∴ required ratio = 624 : 600 = 26 : 25

2) The ratio of the present age of sunitha and vinitha is 4 : 5. Six years hence the ratio of their age will be 14 : 17. What will be the ratio of their age 12 years hence?

a) 15 : 19

b) 13 : 15

c) 16 : 19

d) 17 : 19

e) None of these

c) 16 : 19

Explanation:

Suppose the present age of sunitha and vinitha be 4x years and 5x years respectively.

Six years hence,

(4x+6)/(5x+6)  =  14/17

Or 68x + 102 = 70 x + 84

Or 2x = 18, ∴ x = 9

Ratio of age of sunitha and vinitha after 12 years

= 4x +12 : 5 x +12 = 36 +12 : 45 + 12

= 48 : 57 = 16 : 19

3) The age of father is three times the age of his son at present. Four years hence the ratio between the age of father and son becomes 13 : 5 respectively. What is the present age of father?

a) 48 years

b) 42 years

c) 52 years

d) Cannot be determined

e) None of these

a) 48 years

Explanation:

present age of son = x years then father`s present age = 3 x years

According to the question

(3x+4)/(x+4) = 13/5 → 15x + 20 = 13 x + 52

2x = 32

∴ x = 16

∴ Present age of father = 3 × 16 = 48 years

4) Mohan and Sohan are 35 and 40 years respectively. After how many years would the ratio of their ages become 9 : 10?

a) 5

b) 10

c) 15

d) Cannot be determined

e) None of these

b) 10

Explanation:

Suppose the required ratio will be obtained after x years

According to question.

(35+x)/(40+x) = 9/10

Or, 350 + 10x = 360 + 9x

∴ x = 10

5) Amar started a business investing ₹ 45,000. Six months later prakash joined him with ₹ 30,000. In what ratio should the profit they earn be distributed at the end of year?

a) 3 : 1

b) 3 : 4

c) 3 :2

e) None of these

a) 3 : 1

Explanation:

Ratio of the equivalent capitals of amar and prakash for 1 month

= 4500 × 12 : 30000 × 6 = 540000 : 180000 = 3 : 1

∴ ratio of profit sharing = 3 : 1

6) A, B and C started a business with investment in the ratio 5 : 6 : 8 respectively. After one year C with drew 50% of his capital and A increased his capital by 60% of his investment. After two years in what ratio should the earned profit be distributed among A, B and C respectively?

a) 2 : 3 : 3

b) 4 : 3 :2

c) 13 : 12 : 12

d) Cannot be determined

e) None of these

c) 13 : 12 : 12

Explanation:

required ratio of A : B : C

= (5X × 12 + 8X × 12 : (6X × 24) : (8X × 12 + 4X × 12)

= (60X + 96X) : (144X) ; (96X +48X)

156 : 144 : 144 = 13 : 12 : 12

7) A particular sum was divided among A, B and C, in the ratio 2:6:7 respectively. If the amount received by A was ₹ 4,908, what was the difference between the amounts received by B and C?

a) ₹ 2, 454

b) ₹ 3, 494

c) ₹ 2,135

d) ₹ 2, 481

e) None of these

a) ₹ 2, 454

Explanation:

If the total amount be ₹ x, then

2x/15 = 4908

X = (4908 ×15)/2 = ₹ 36810

∴ required difference

= (7-6)/15  ×36810= ₹ 2454

8) The average  age of a man and his son is 30 years. The ratio of their ages four  years ago was 10 : 3 respectively. What is the difference between the present ages of the man and his son?

a) 28 years

b) 16 years

c) 26 years

d) 44 years

e) None of these

a) 28 years

Explanation:

Four years ago,

father`s age = 10x years

son`s age = 3x years

∴ 10x + 3x +8 = 60

[Sum of their ages = 2 × 30 = 60]

13x = 60 – 8 = 52

X = 4

∴required difference

= 7x = 7 × 4 = 28 years

9) The ratio between Glria`s and Sara`s present ages is 4 : 7 respectively, two years ago the ratio between their ages was 1 : 2 respectively. What will be Sara`s age three years hence?

a) 17 years

b) 14 years

c) 11 years

d) 8 years

d) None of these

a) 17 years

Explanation:

let Gloria`s and sara`s present agaes be 4x and 7x years respectively

Two years ago,

(4x-2)/(7x-2)=1/2

8x – 4= 7x -2

X = 2

∴ sara`s age three years hence = 7x + 3

= 17 years

10) The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743 : 842 respectively, what is the total number of girls in the school?

a) 14860

b) 16480

c) 15340

d) Cannot be determined

e) None of these

e) None of these

Explanation:

Boys : girls = 743 : 842

Total number of students

=31700

∴ number of girls

= 842/((743+842))  × 31700

= 842/1585 ×31700

= 16840