Question

A train $X$ starts from New Delhi at $4$ pm and reaches Ghaziabad at $5$ pm. While another train $Y$ starts from Ghaziabad at $4$ pm and reaches New Delhi at $5:30$ pm. At what time will the two trains cross each other?

• A. $4:30$ pm
• B. $4:24$ pm
• C. $4:36$ pm
• D. $4:41$ pm

Answer 1

The correct option is C $4:36$ pm

Let the distance between Meerut and Ghaziabad be $d$ km

First train covers distance $d$ km in $1$ hr

Speed of first train $=d$ km/hr

Second train covers distance $d$ km in $1\frac{1}{2}=\frac{3}{2}$ hr.

Speed of second train $=\frac{d}{\frac{3}{2}}=\frac{2d}{3}$ km/hr.

Let the train meet $x$ hours after $4$ pm

Distance travelled by first train in $x$ hours $=x\times d$ km

Distance travelled by second train in $x$ hours $=x\times \frac{2d}{3}$ km

Sum of these distances must be the total distance between Meerut and Ghaziabad

$x\times d+x\times \frac{2d}{3}=d$

$\Rightarrow x+\frac{2x}{3}=1$

$\Rightarrow \frac{5x}{3}=1$

$\Rightarrow x=\frac{3}{5}$ hr $=36$ min

i.e., the trains will cross each other at $4:36$ pm.