Question

Kiran is 24 years older than Rakesh. 10 years back Kiran’s age was five times the age of Rakesh. Find the present age of Rakesh.
A. $40$years
B. $16$ years
C. $20$years
D. $36$ years

Answer 1

Such a type of question can be solved by assuming one person's age as $x$ and getting the equation of second person’s age in terms of $x$. So let’s assume Age of Rakesh as $x$. As Kiran is 24 years older than Rakesh, so Kiran’s present age is $x + 24$. 10 years ago Kiran’s age was five times the age of Rakesh. So, $(x + 14) = 5(x - 10)$. Solve this equation to get the value of $x$. This is the age of Ramesh.

Complete step-by-step answer:
To solve such a type question assume one person's age as $x$and getting the equation of second person’s age in terms of $x$. So let’s assume Age of Rakesh as $x$.
Kiran is 24 years older than Rakesh. So Kiran’s present age is $x + 24$.
10 years ago Kiran’s age was five times the age of Rakesh.
10 years ago Kiran’s age was $x + 24 - 10 = x + 14$.
10 years ago Rakesh’s age was $x - 10$.
As 10 years ago Kiran’s age was five times the age of Rakesh so we can write as $(x + 14) = 5(x - 10)$.
So, $(x + 14) = 5(x - 10)$
Simplifying, $x + 14 = 5x - 50$
Taking all $x$ terms on right side and constant terms on left side of the equation,
So, $50 + 14 = 5x - x$
So, $64 = 4x$
Arranging the terms, $4x = 64$
Dividing the equation by 4 on both side, $\dfrac{{4x}}{4} = \dfrac{{64}}{4}$
So, $x = 16$.
So, Rakesh’s present age is 16 years.

So, option (B) is the correct answer.

Note: In the above question if the present age of Kiran was asked then we can calculate as Kiran’s present age is given by $x + 24$. So Kiran’s present age is $16 + 24 = 40$ years. This question can also be solved by assuming the age of Kiran as $x$ and converting the age of Rakesh in terms of $x$ as per the conditions given.