Question

A train $M$ leaves Meerut at $5$ $a.m.$ and reaches Delhi at $9$ $a.m.$ Another train $N$ leaves Delhi at $7$ $a.m.$ and reaches Meerut at $10.30$ $a.m.$ At what time does the two trains cross each other?

• A. $7.36$ $a.m.$
• B. $7.56$ $a.m.$
• C. $8$ $a.m.$
• D. $8.26$ $a.m.$

Answer 1

Answer: (B)

$7.56$ $a.m.$

Let the distance between Meerut and Delhi be $x$ km and let the trains meet y hours after $7$ a.m.

Clearly, M covers $x$ km in $4$ hrs and N covers $x$ km in ($\frac{7}{2}$) hrs.

Speed of M =$\frac{x}{4}$km\hr Speed of N =$\frac{2x}{7}$km\hr

Distance covered by M in$(y+2)$ hrs + Distance covered in $y$ hrs = $x$.

$\therefore \frac{x}{4}(y+2)+\frac{2x}{7}y=x\Rightarrow \frac{y+2}{4}+\frac{2y}{7}=1\Rightarrow y=\frac{14}{15}hr=\frac{14}{15}\times 60=56min$

Hence,the train meet at $7.00+0.56=7.56am$