Question

Rajesh commutes daily by traveling $\frac{4}{5}$ of the distance between his home and office by metro train, $\frac{3}{20}$ by auto and remaining $1km$ on foot. What is the distance between his home and office?

Answer 1

Let $x$ be distance between Rajesh’s home and office.

Distance traveled by Rajesh is given as –

$$\begin{gathered} x=\frac{4x}{5}+\frac{3x}{20}+1 \\ \Rightarrow x-\frac{4x}{5}-\frac{3x}{20}=1 \\ \Rightarrow \frac{20x-16x-3x}{20}=1 \\ \Rightarrow \frac{x}{20}=1 \\ \Rightarrow x=20km \end{gathered}$$

Hence the distance between home and office of Rajesh is $20km.$