Question : Directions: The ratio of the present ages of P and Q is 5 : 8. Three years later their ages will be in the ratio 8 : 11. What is the present age (in years) of Q?
Option 1: 5
Option 2: 11
Option 3: 14
Option 4: 8
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Correct Answer: 8
Solution :
Given:
The ratio of the present ages of P and Q is 5 : 8.
Let the present age of P be 5y and the present age of Q be 8y.
Age of P after 3 years = 5y + 3
Age of Q after 3 years = 8y + 3
The ratio of their ages after 3 years is 8 : 11
⇒ $\frac{5y\ +\ 3}{8y\ +\ 3}=\frac{8}{11}$
⇒ 11 × (5y + 3) = 8 × (8y + 3)
⇒ 55y + 33 = 64y + 24
⇒ 64y – 55y = 33 – 24
⇒ 9y = 9
⇒ y = 1
So, Q's present age = 8y = 8 × 1 = 8 years. Hence, the fourth option is correct.
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