Question

The total ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was \[2:3:4\]. What is the present age of Saransh?
A) 24 years
B) 32 years
C) 34 years
D) 38 years

Answer 1

Hint: The actual ages of the three persons would be the given ratio multiplied by some constant. Assume a constant multiplying factor for the ratio, add their sum to given value and find the required answer.

Complete step-by-step answer:
We have been given the sum of the ages of Jayant, Prem and Saransh which is 93 years. We also have the ratio of their ages 10 years ago. Let us assume the constant multiplying factor for the ratios is the variable $x$. So now we can write the actual ratio of their ages. The ratio of their ages ten years ago would be $2x:3x:4x$.
Now the ratio of the present age would be their ages ten years ago plus 10. So the ratio of their present ages would be $2x + 10:3x + 10:4x + 10$.
We also know that the sum of their present ages is 93 years. So, using that information we get,
$
  2x + 10 + 3x + 10 + 4x + 10 = 93 \\
  9x + 30 = 93 \\
  9x = 63 \\
  x = 7 \\
$
Thus, we now have the value of the constant multiplying factor.
So, the ages of Jayant, Prem and Saransh ten years back would be 14 years, 21 years and 28 years respectively.
So, their present ages that is after ten year would be 24 years, 31 years and 38 years respectively.
So, Saransh’s present age is 38 years
So, the correct option is option D

Note: This is a relatively easy problem of ratio proportion. The only catch in this problem is to see whether the ratio is given of the present ages or not.