Question

Rahul covers a distance from $P$ to $Q$ on bicycle at $10km/h$ and returns back at $9km/h$. Anuj covers the distance from $P$ to $Q$ and $Q$ to $P$ both at $12km/h$. On calculation , find that Anuj took $10$ minutes less than Rahul. Find the distance between $P$ and $Q$.

Answer 1

$Time=\frac{Distance}{speed}$

Total time taken by Rahul = $\frac{x}{10}+\frac{x}{9}$

$=\frac{9x+10x}{90}=\frac{19x}{90}$ ___ (1)

Total time taken by Anuj = $\frac{x}{12}+\frac{x}{12}=\frac{2x}{12}=\frac{x}{6}$ ___ (2)

A.t.Q:-

Rahul takes more time :

$\therefore \frac{19x}{90}-\frac{x}{6}=10\Rightarrow \frac{19x-15x}{90}=\frac{10}{1}\Rightarrow 4x=900$

$\Rightarrow x=\frac{900}{4}=225$

$\therefore$ Distance b/w P and Q is $225$ km.