Question

A and B are friends and B is 2 years younger than A. A's father D is twice as old as A and B is twice as his sister C. The age of D and C differ by 40 years. The ages of 'A' and 'B' are respectively
1. 26 yrs., 24 yrs.
2. 25 yrs., 23 yrs.
3. 30 yrs., 28 yrs.
4. None of these

Answer 1

Correct Answer - Option 1 : 26 yrs., 24 yrs.

Given:

B is 2 years younger than A,

A's father D is twice as old as A,

B is twice as his sister C,

The age of D and C differ by 40 years.

Calculation:

According to the question,

B is 2 years younger than A,

⇒ B = A - 2      ----(1) 

A's father D is twice as old as A,

⇒ D = 2A      ----(2)

B is twice as his sister C,

⇒ B/2 = C      ----(3)

The age of D and C differ by 40 years, 

⇒ D - C = 40      ----(4)

Now substitute (2) & (3) in equation (4)

⇒ 2A - (B/2) = 40

⇒ 4A - B = 40 × 2

⇒ 4A - B = 80      ----(5)

Now (5) - (1)

⇒ 3A = 78

⇒ A = 26 

Now substitute Value of A in (1)

⇒ B = 26 - 2

⇒ B = 24

∴ The ages of 'A' and 'B' are 26 yrs & 24 yrs respectively.