Four years ago, Shyam's age was 3/4 times of that of Ram. Four years hence, Shyam's age will be 5/6 times that of Ram. Find the present age of Shayam.

A 16 years

B 32 years

C 18 years

D 22 years

E None of these

Correct Answer: Option A

4 years ago, let Ram's age = x years and

Shyam's age = 3x/4 years

Now, Ram's present age = (x + 4) years

And Shyam’s present age = {(3/4)x + 4} years

Now, according to the question,

\(\frac{5}{6}\left( {x + 4 + 4} \right) = \left( {\frac{3}{4}x + 4 + 4} \right)\)

⇒ 4 (5x + 40) = 6(3x + 32)

⇒ 20x + 160 = 18x + 192

⇒ 2x = 32

⇒ x = 16

Hence, present age of Shyam = (3/4) × 16 + 4 = 16 years.

Hence, the required answer is 16 years