Question

Two trains P and Q start simultaneously in the opposite direction from two points A and B and arrive at their destinations 25 and 16 hours respectively after their meeting each other. At what speed does the second train Q travel if the first train travels at 100 km/h?

• A. \(100 \text{ km/hr} \)
• B. \(125 \text{ km/hr} \)
• C. \(120 \text{ km/hr} \)
• D. \(140 \text{ km/hr} \)

Hint:

This specific "post-meeting time" formula is a massive time-saver for competitive exams. Remember: The speed ratio is the inverse square root of the time ratio.

Answer 1

The Correct Option is B

Concept: When two objects start simultaneously from two points and move towards each other, and after meeting they reach their opposite destinations in time \(T_1\) and \(T_2\), the ratio of their speeds \(S_1\) and \(S_2\) is given by: \[ \frac{S_1}{S_2} = \sqrt{\frac{T_2}{T_1}} \]
Identify given values and substitute into the formula.
Here, speed of train P (\(S_1\)) = 100 km/h.
Time taken by train P after meeting to reach B (\(T_1\)) = 25 hours.
Time taken by train Q after meeting to reach A (\(T_2\)) = 16 hours.
Let the speed of train Q be \(S_2\). \[ \frac{100}{S_2} = \sqrt{\frac{16}{25}} \] \[ \frac{100}{S_2} = \frac{4}{5} \] \[ 4S_2 = 500 \quad \Rightarrow \quad S_2 = 125 \text{ km/hr}. \]