Question : Four years ago, Shyam's age was $\frac{3}{4}$th times that of Ram. Four years hence, Shyam's age will be $\frac{5}{6}$th times that of Ram. What is the present age of Shyam?
Option 1: 24 years
Option 2: 20 years
Option 3: 16 years
Option 4: 15 years
Correct Answer: 16 years
Solution :
Given: Four years ago, Shyam's age was $\frac{3}{4}$th times that of Ram.
Four years ago, assume the ages of Ram and Shyam were $4x$ and $3x$.
Four years hence, Shyam's age will be $\frac{5}{6}$th times that of Ram.
According to the question,
$\frac{4x+8}{3x+8}=\frac{6}{5}$
⇒ $20x+40=18x+48$
⇒ $20x-18x=48-40$
⇒ $2x=8$
⇒ $x=4$
The present age of Shyam $=3x+4=3\times 4+4= 16$ years
Hence, the correct answer is 16 years.
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