Question

Rajan got married 8 years ago. His present age is $\dfrac{6}{5}$ his age at the time of his marriage. Rajan’s sister was 10 years younger to him at the time of his marriage. The present age of Rajan’s sister is
$
  (A)\,32\,years \\
  (B)\,36\,years \\
  (C)\,38\,years \\
  (D)\,34years \\
$

Answer 1

Hint: Find present age of Rajan and with that context find his sister’s age. First, we are going to consider Rajan’s age 8 years ago as $x$and then from the statements of the question we will form an equation, from which will find the value of $x$,which is the present age. Then we form the equation for finding his sister's age and find it and then add accordingly to find the present age.

Complete step-by-step solution:
Let us consider the age of Rajan 8 years ago as $x$
Then his present age will be $(x + 8)$ years
From the question, we know that his present age is $\dfrac{6}{5}$ his age at the time of his marriage. So,
$x + 8 = \dfrac{6}{5}x$
We are going to solve this equation for $x$
$
 \Rightarrow 5x + 40 = 6x \\
  \Rightarrow x = 40 \\
$
So, we have found Rajan's age 8 years ago and we can find the age of his sister 8 years ago.
So, it will be
$\Rightarrow 40 - 10 = 30\,years$
Now, let us find the present age of his sister
$\Rightarrow 30 + 8 = 38\,$years

Therefore, the present age of Rajan’s sister is 38 years i.e, option ‘C’

Note: We have to read the statements given in the question, while forming the equation and think whether considering the present age or 8 years ago age as x based on the scenario such that the problem gets solved easily.