Question

‘A’ and ‘B’ are two stations 465 km apart. A train starts from ‘A’ at 10 a.m. and travels towards ‘B’ at 65 kmph. Another train starts from ‘B’ at 11 a.m. and travels towards ‘A’ at 35 kmph. At what time do they meet?

• A. 3:00 a.m.
• B. 3:00 p.m.
• C. 3:05 a.m.
• D. 3:05 p.m.

Hint:

For opposite-direction motion: \[ \text{Relative Speed} = v_1+v_2 \]

Answer 1

The Correct Option is D

Concept: When two objects move towards each other, \[ \text{Relative Speed} = \text{Sum of Speeds} \]

Step 1: Distance covered by first train before 11 a.m.
The first train moves for 1 hour. \[ 65 \times 1 = 65 \text{ km} \] Remaining distance: \[ 465-65=400 \text{ km} \]

Step 2: Find relative speed.
\[ 65+35=100 \text{ kmph} \]

Step 3: Find meeting time after 11 a.m.
\[ \frac{400}{100}=4 \text{ hours} \]

Step 4: Determine clock time.
\[ 11:00 \text{ a.m.}+4 \text{ hours} = 3:00 \text{ p.m.} \] \[ \boxed{3:00 \text{ p.m.}} \] Hence option (B) is correct.