Question : The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:
Option 1: 30 years
Option 2: 32 years
Option 3: 40 years
Option 4: 35 years
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Correct Answer: 35 years
Solution :
Let the present ages of A and B be 3$x$ and 5$x$ respectively.
According to the question,
$\frac{(3\text{x} + 5)}{(5\text{x} + 5)} = \frac{13}{20}$
⇒ 60$x$ + 100 = 65$x$ + 65
⇒ 5$x$ = 35
⇒ $x$ = 7
The present age of B = 5$x$ = 5 × 7 = 35
$\therefore$ The present age of B is 35 years.
Hence, the correct answer is 35 years.
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