Question

A train leaves a station A at $7$ am and reaches another station $B$ at $11$ am. Another train leaves B at $8$ am and reaches A at $11.30$ am. The two trains cross one another at

• A. $8.36$ am
• B. $8.56$ am
• C. $9.00$ am
• D. $9.24$ am

Answer 1

Answer: (D)

$9.24$ am

Let the distance between station A and station B is $x$ km.

Given first train starting from A will take $4$ hours to cover $x$ km and the second train starting from B takes 3.5 hours to cover the $x$ km.

Therefore, speed of the train is $\frac{x}{4}$ km/hr and $\frac{x}{\frac{7}{2}}$ or $\frac{2x}{7}$ km/hr respectively.

Let both the train meet t hours after $8$ am.

Then first train (starting from A) would have travelled (t+1) hours whereas the second train (starting from B) would have travelled t hours. Therefore, distance travelled by them would be $\frac{x(t+1)}{4}$ km and $\frac{2xt}{7}$ km respectively.

Clearly, when both the trains met the distance travelled by them will be x km.

Therefore,

x = $\frac{x(t+1)}{4}$ + $\frac{2xt}{7}$

or, $1=\frac{t+1}{4}$ + $\frac{2t}{7}$

or, $28=7t+7+8t$

or, $t=\frac{21}{15}$ hours or $\frac{7}{5}$ hours or 1 hour and $24$ minutes

Therefore, the trains will met at 9:24 am.

Hence, (D) is the correct answer.