Question

Eight years ago, P was half of Q in age. If the ratio of their present ages is 2 ∶ 3, What will be the total of their present ages?
1. 35
2. 16
3. 24
4. 40

Answer 1

Correct Answer - Option 4 : 40

Ration of Present age of P and Q = 2 : 3

Assume;

Age of P = 2P

Age of Q = 3P

Eight years ago;

Age  of P = (2P - 8) years

Age of Q = (3P - 8) years

Age of P = Q/2

⇒ (2P - 8) = (3P - 8)/2

⇒ 2 × (2P - 8) = (3P - 8)

⇒ 4P - 16 = 3P - 8

⇒ 4P - 3P = 16 - 8

⇒ P = 8

So, 

Age of P = 2P = 16 years

Age of Q = 3P = 24 years

Sum of age of P and Q = 16 + 24

= 40 years

Hence, "40" is the correct answer.