Question

the ages of A and B are in the ratio 5:7, five
years ago their age were in the ratio 7:13,find their age​

Answer 1

Given :

• Ratio of the age of A and B = 5 : 7
• Ratio of their ages before 5 years = 7 : 13

To find :

• Present age of A and B.

Solution :

Let,

• Present age of A = 5x years
• Present age of B = 7x years

Their ages ago five years :-

→ Age of A = 5x - 5 years

→ Age of B = 7x - 5 years

According to the question,

⇒ (5x - 5)/(7x - 5) = 7/13

⇒ 13(5x - 5) = 7(7x - 5)

⇒ 65x - 65 = 49x - 35

⇒ 65x - 49x = - 35 + 65

⇒ 16x = 30

⇒ x = 30/16

⇒ x = 1.875

Substituting the value of 'x' in the present ages of A and B :-

→ Present age of A = 5x

→ Present age of A = 5(1.875)

→ Present age of A = 9.375 years

→ Present age of B = 7x

→ Present age of B = 7(1.875)

→ Present age of B = 13.125 years