Question

Ram's age is $ \dfrac{1}{3} $ rd of his father's age. Ram's father's age in 12 years will be 12 years more than twice of Shyam's age after 10 years. If Shyam's eighth birthday was celebrated 3 years before, then what is Ram's age at present
A. 14 years
B. 16 years
C. 11 years
D. 13 years

Answer 1

Hint: Shyam’s eighth birthday was celebrated 3 years before, so his present age will be $ 8 + 3 = 11 $ years. In ten years, Shyam’s age will be 21 years. So Ram’s father’s age will be 12 more than twice of 21 years. From this find Ram’s father’s age and then Ram’s age.

Complete step-by-step answer:
We are given that Ram's age is $ \dfrac{1}{3} $ rd of his father's age and Ram's father's age will be 12 years more than twice of Shyam's age after 10 years where Shyam's eighth birthday was celebrated 3 years before.
Shyam’s eighth birthday was 3 years before, which means he is now 3 years older than 8.
So Shyam’s present age is $ 8 + 3 = 11 $ years.
Let Ram’s father’s age be x.
Ram’s father’s age will be 12 years more than twice of Shyam's age after 10 years.
After 10 years Shyam’s age will be $ 11 + 10 = 21 $ years.
So x will be 12 more than twice of 21 years
 $\Rightarrow x = 12 + 2\left( {21} \right) = 12 + 42 = 54 $
Therefore, Ram’s father’s age in 12 years is 54 years.
So his present age will be $ 54 - 12 = 42 $ years.
Ram’s age is $ \dfrac{1}{3} $ rd of his father's age. This means Ram’s age is $ \dfrac{1}{3} $ rd of 42 years
 $ \Rightarrow \dfrac{1}{3} \times 42 = 14 $ years.
Therefore, Ram’s present age is $ 14 \;years $ .
So, the correct answer is “Option A”.

Note: Instead of finding Ram’s father’s age and then Ram’s age, we can directly find Ram’s age from Shyam’s age. Let Ram’s age be x then it will be one-third of Ram’s father’s age. So Ram’s father’s age will be thrice of Ram’s age, 3x. So we can directly substitute 3x and find the value of x, which is Ram’s age.