Question

15. The ages of A and B are in the ratio 5 : 2. After 5 years, their ages will be in the ratio 15: 7.
The present age of A is
(a) 48 years
(b) 36 years
(c) 40 years
(d) 35 years
​

Answer 1

Step-by-step explanation:

let the present ages of A=5x and

B=2x

after 5 years the ages of A =5x+5 and

B=2x+5

after 5 years the ratios of A and B is

(5x+5)/(2x+5)=15/7

=>7(5x+5)=15(2x+5)

=>35x+35=30x+75

=>5x=40

=>x=8

so the present age of A=5x=5×8=40 years(option C)

Answer 2

Answer :

• Age of A = 40 years.
• Age of B = 16 years.

Given :

• The ages of A and B are in the ratio 5 : 2 and after 5 years, their ages will be in the ratio 15 : 7.

To Find :

• Ages of A and B.

Solution :

Put x in the ratio

Now

• Age of A = 5x
• Age of B = 2x

After 5 years

• Age of A = (5x + 5)
• Age of B = (2x + 5)

It is given that

• After 5 years, their ages will be in the ratio 15 : 7.

According to question :

→ 5x + 5/2x + 5 = 15/7

→ 7 (5x + 5) = 15 (2x + 5)

→ 35x + 35 = 30x + 75

→ 35x - 30x = 75 - 35

→ 5x = 40

→ x = 40/5

→ x = 8

Now

• Age of A = 5x = 5(8) => 40 years
• Age of B = 2x = 2(8) => 16 years

Hence, the ages of A and B are 40 years and 16 years.