Question

Mohan, Sohan and Mahesh are standing in a queue. Mohan’s height is $\dfrac{10}{9}$ of the height of Sohan, Sohan’s height is $\dfrac{3}{4}th$ of the height of Mahesh. If Mahesh’s height is 180cm, find the height of Sohan.

Answer 1

Hint: We start solving this question by converting the given information into equations. First, we write an equation between the height of Mohan and height of Sohan. Then we write another equation between the height of Sohan and the height of Mahesh. Then we substitute the height of the Mahesh in the obtained equation to find the height of Sohan.

Complete step-by-step answer:
We are given that the height of Mohan is $\dfrac{10}{9}th$ of the height of Sohan.
We are also given that the height of Sohan is $\dfrac{3}{4}th$ of the height of Mahesh.
Height of Mahesh is equal to 180cm.
We need to find the height of Sohan.
Let us assume that the height of Sohan is h.
As we are given that the height of Mohan is $\dfrac{10}{9}th$ of the height of Sohan, we can write height of Mohan as,
$\begin{align}
  & \Rightarrow \text{Height of Mohan}=\dfrac{10}{9}\left( \text{Height of Sohan} \right) \\
 & \Rightarrow \text{Height of Mohan}=\dfrac{10}{9}h \\
\end{align}$
As we are given that height of Sohan is $\dfrac{3}{4}th$ of the height of Mahesh, so we can write height of Sohan as,
$\Rightarrow \text{Height of Sohan}=\dfrac{3}{4}\left( \text{Height of Mahesh} \right)$
As we are given that the height of Mahesh is 180cm. So, by substituting the value of height of Mahesh in the above equation (1), we get
$\begin{align}
  & \Rightarrow h=\dfrac{3}{4}\left( 180 \right) \\
 & \Rightarrow h=3\times 45 \\
 & \Rightarrow h=135 \\
\end{align}$
So, we get that h is equal to 135cm.
Hence, we get that the height of Sohan is equal to 135cm.
Hence, the answer is 135cm.

Note: The common mistake that one does while solving this type of problem is one might take the equations wrong as
$\Rightarrow \text{Height of Sohan}=\dfrac{10}{9}\left( \text{Height of Mohan} \right)$
$\Rightarrow \text{Height of Mahesh}=\dfrac{3}{4}\left( \text{Height of Sohan} \right)$
So, one should carefully read and understand the given statements before converting them into equations.