Question

The age of Manoj after 15 years is 4 times the age of that 15 years before. His present age is
(a) 10 years
(b) 15 years
(c) 20 years
(d) 25 years

Answer 1

Hint: Here, first of all we will assume that the present age of Manoj is equal to x. Then, we will find his age 15 years ago by subtracting 15 from his present age. Similarly, we will find his age 15 years after by adding 15 years to his present age. Thereafter, we will equate his age after 15 years to 4 times his age 15 years ago to obtain a linear equation in x. On solving this equation we will find the value of x which is also equal to his present age.

Complete step-by-step answer:
Let us consider that the present age of Manoj = x years
So, his age after 15 years from now = (x+ 15) years ………(1)
And, his age 15 years ago from now = (x – 15 ) years
So, the 4 times of his age 15 years ago = $4\left( x-15 \right)=\left( 4x-60 \right)years..........\left( 2 \right)$
Since, it is given that his age after 15 years from now is equal to 4 times of his age 15 years ago.
Therefore, we can equate equations (1) and (2). So, we get:
 $\begin{align}
  & x+15=4x-60 \\
 & \Rightarrow 15+60=4x-x \\
 & \Rightarrow 3x=75 \\
 & \Rightarrow x=\dfrac{75}{3}=25 \\
\end{align}$
So, the value of x comes out to be 25, which means that the present age of Manoj is equal to 25 years.
Hence, option (d) is the correct answer.

Note: Students should be careful while forming the equation. Since, it is given that his age 15 years from now is equal to 4 times of his age 15 years ago which means that we have to multiply 4 with his age 15 years ago and then equate it to his age 15 years from now. If by mistake we do the opposite multiply then it will give the wrong result.