Question

The sum of ages of Rajesh and his nephew is 50 yrs. Seven years ago the product of their ages was 4 times Rajesh's age at that time. The present ages of Rajesh and his nephew are?
1. 11yrs, 39 yrs
2. 8 yrs, 42 yrs
3. 39 yrs, 11 yrs
4. 42 yrs, 8 yrs
5. 26 yrs, 24 yrs

Answer 1

Correct Answer - Option 3 : 39 yrs, 11 yrs

Given:

Sum of ages of Rajesh and his nephew = 50 yrs

7 years ago, the product of their ages = 4 × (7 years ago, Rajesh's age)

Calculation:

Let the present age of Rajesh be x yrs.

And the present age of his nephew = (50 - x) yrs

Now, 7 years ago, age of Rajesh = (x - 7) yrs

And 7 years ago, age of his nephew = (50 - x - 7) yrs

⇒ (43 - x) yrs

According to the question,

(x - 7)(43 - x) = 4(x - 7)

⇒ 43 - x = 4 

⇒ x = 39

Hence, the present age of Rajesh = 39 yrs

And the present age of his nephew = (50 - 39) yrs

⇒ 11 yrs

∴ The present ages of Rajesh and his nephew are 39 yrs and 11 yrs respectively.