Mary is 12 years younger to Pinky. After 3 years, the ratio of their ages will be 5:8. If the present age of Sam is the sum of ages of Mary and Pinky, then what was the age of Sam 15 years back ?

A 31 years

B 37 years

C 46 years

D 29 years

Correct Answer: Option A

Let the present age of Pinky be x years

Then the age of Mary is x - 12 years

After 3 years,

Ratio of \(\frac{Mary}{Pinky}\;=\;\frac{\mathrm x\;-\;9}{\mathrm x\;+\;3}\;=\;\frac58\)

8x - 72 = 5x +15

=> 3x = 87

=> x = 29

=> Age of Pinky = 29 years

=> Age of Mary = 29 - 12 = 17 years

Present age of Sam = 29 + 17 = 46

Before 15 years Sam age = 46 - 15 = 31 years.