Question

Hitesh is 40 years old and Rohit is 60 years old. How many years ago was the ratio of their ages 3:5?
A. 5 years
B. 10 years
C. 20 years
D. 37 years

Answer 1

Hint: In this question, we are given present ages of Hitesh and Rohit and we have to find how many years ago their ages were in ratio 3:5. For solving this, we will first suppose the number of years that we have to find as some variable. Using this variable, we will subtract it from present ages and obtain the ratio of their ages. Since the ratio given is 3:5, so both will be equal and hence using the equation formed, we will find the value of the supposed variable. This variable will give us the final answer.

Complete step by step answer:
Here, the present age of Hitesh and Rohit are given and we have to find how many years ago their ages were in ratio 3:5.
Present age of Hitesh is given as 40 years old.
Present age of Rohit is 60 years old.
Let us suppose that, x years ago the ratio of their age was 3:5.
So x years ago, the age of Hitesh became (40-x) years and the age of Rohit (60-x) years.
Since, we are given a ratio of their ages 'x' years ago. So let us find the ratio by our supposed ages.
Ratio of ages of Hitesh and Rohit x years ago becomes 40-x : 60-x. But we are given a ratio as 3:5.
Hence, both are equal, comparing them we get $\dfrac{40-x}{60-x}=\dfrac{3}{5}$.
Let us solve this equation to find the value of x. Cross multiplying we get:
$5\left( 40-x \right)=3\left( 60-x \right)$.
Simplifying the equation we get:
$200-5x=180-3x$.
Taking variables on one side and constant on other side, we get:
$\begin{align}
  & -5x+3x=180-200 \\
 & \Rightarrow -2x=-20 \\
\end{align}$
Cancelling negative sign both sides, we get:
$2x=20$.
Dividing both sides by 2 we get:
$\begin{align}
  & x=\dfrac{20}{2} \\
 & \Rightarrow x=10 \\
\end{align}$
Hence, x = 10 is the required number of years.
Therefore, 10 years ago the ratio of ages of Hitesh and Rohit was 3:5.

So, the correct answer is “Option B”.

Note: Students should take care while taking ratio. Given the ratio is smaller to a bigger number, therefore, we will take 40-x to 60-x because only this can become 3:5. Take care while cross multiplying and solving the value of x. Students should try not to make mistakes while adding and subtracting.