Question

The difference between the ages of two men is 10 years, 15 years ago, the elder one was twice as old as the younger one. The present age of the elder man is
1. 25 years
2. 35 years
3. 45 years
4. 40 years

Answer 1

Correct Answer - Option 2 : 35 years

Given :

The difference between the ages of two men = 10 years

15 years ago, the ratio of elder man to younger man = 2 ∶ 1

Calculations : 

Let the present age of elder man be 'a'

The present age of a younger man be 'b'

According to the question,

15 years ago the age of elder man = a - 15

15 years ago the age of younger man = b - 15

a - b = 10 

⇒ a = b + 10 

The ratio of ages of the elder man and younger man = (a -15) ∶ (b - 15)

(a -15) / (b - 15) = 2 / 1

⇒ 1 × (a - 15) = 2 × (b - 15) 

⇒ a - 15 = 2b - 30

⇒ a - 2b = -30 + 15

⇒ b + 10 - 2b = -15

⇒ -b = -15 -10 

⇒ b = 25 

a = b + 10 

⇒ a = 25 + 10                   (∵ a = b + 10 )

Hence a = 35 years

∴The elder man age is 35 years