Govt. Exams
Entrance Exams
When two objects move towards each other from different starting points and times, we find their meeting point by calculating the distance each covers until they meet.
Step 1: Calculate distance covered by Train A before Train B starts
Train A leaves at 6:00 AM and Train B leaves at 8:00 AM — a 2-hour head start.
\[
\text{Distance by Train A in 2 hours} = 75 \times 2 = 150\,\text{km}
\]
Remaining distance between trains at 8:00 AM:
\[
500 - 150 = 350\,\text{km}
\]
Step 2: Find relative speed of approach
Both trains now move towards each other. Their combined closing speed is:
\[
\text{Relative speed} = 75 + 85 = 160\,\text{km/h}
\]
Step 3: Calculate time to meet after 8:00 AM
Time for both trains to cover the remaining 350 km:
\[
\text{Time} = \frac{350}{160} = \frac{35}{16}\,\text{hours}
\]
Converting to hours and minutes:
\[
\frac{35}{16} = 2\frac{3}{16}\,\text{hours} = 2\,\text{hours} + \frac{3}{16} \times 60\,\text{minutes}
\]
\[
\frac{3}{16} \times 60 = 11.25\,\text{minutes} = 11\,\text{minutes and 15 seconds}
\]
Step 4: Add elapsed time to 8:00 AM
Meeting time:
\[
8:00\,\text{AM} + 2\,\text{hours}\,11\,\text{minutes}\,15\,\text{seconds} = 10:11:15\,\text{AM}
\]
Answer: The trains meet at \(10:11:15\,\text{AM}\) (Option A)
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