Question

$P$ and $Q$ are two railways stations which are $560$ km apart. An express train leaves stations $P$ to stations $Q$ at a speed of $55$ km/hr and a passenger train leaves station $Q$ to station $P$ at a speed of $25$ km/hr, both at the same time. Find when and where will the both trains meet.

• A. After $4$ hours at a distance of $325$ km from station $P$
• B. After $7$ hours at a distance of $385$ km from station $P$
• C. After $5$ hours at a distance of $295$ km from station $P$
• D. After $8$ hours at a distance of $345$ km from station $P$

Answer 1

The correct option is B After $7$ hours at a distance of $385$ km from station $P$

Let's assume that the train $P$ travels $x$m before they meet.

Then $Q$ travels $(560-x)$m.

Time $=\frac{\text{Distance}}{\text{Speed}}$

Time taken for $P$ $=$ Time taken for $Q$

$\Rightarrow \frac{x}{55}=\frac{560-x}{25}$

$\Rightarrow 25x=30800-55x$

$\Rightarrow$ $80x=30800$

$\Rightarrow x=385$ km
So, time from station $P$ $=\frac{385}{55}=7$ hours.