Question

Two non-stop express trains A and B run between two stations P and Q. A starts at 2:00 pm and runs at a uniform speed of 70 kmph, whereas B starts at 3:30 pm and runs at a uniform speed of 85 kmph. At what time do both A and B reach Q?

• A. 11:00 pm
• B. 10:30 pm
• C. 10:00 pm
• D. 9:45 pm

Hint:

For same-distance problems, use: \[ \text{Distance}=\text{Speed}\times\text{Time} \] and equate the distances traveled.

Answer 1

The Correct Option is A

Concept: Since both trains reach station Q at the same instant, the distances covered by both are equal.

Step 1: Let the common arrival time be \(t\) hours after 2:00 pm. Then train A travels for \[ t \] hours. Train B starts 1.5 hours later. Hence B travels for \[ t-1.5 \] hours.

Step 2: Equate distances. Distance covered by A: \[ 70t \] Distance covered by B: \[ 85(t-1.5) \] Since both travel between the same stations, \[ 70t=85(t-1.5) \] \[ 70t=85t-127.5 \] \[ 15t=127.5 \] \[ t=8.5 \]

Step 3: Determine arrival time. 8.5 hours after 2:00 pm: \[ 2:00\text{ pm}+8\text{ h }30\text{ min} \] \[ =10:30\text{ pm} \] Therefore, \[ \boxed{10:30\text{ pm}} \]