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The Sabarmati Express left Ahmedabad for Mumbai. Having travelled 300 km, which constitutes 66.666 per cent of the distance between Ahmedabad and Mumbai, the train was stopped by a red signal. Half an hour later, the track was cleared and the engine-driver, having increased the speedby 15 km per hour, arrived at Mumbai on time. Find the initial speed of the Sabarmati Express.
  • a)
    50 kmph
  • b)
    60 kmph
  • c)
    75 kmph
  • d)
    40 kmph
Correct answer is option 'B'. Can you explain this answer?
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The Sabarmati Express left Ahmedabad for Mumbai. Having travelled 300 ...
By increasing speed by 15 kmph, the time reduces by 30 minutes.
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The Sabarmati Express left Ahmedabad for Mumbai. Having travelled 300 ...
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The Sabarmati Express left Ahmedabad for Mumbai. Having travelled 300 ...
Given information:
- Distance between Ahmedabad and Mumbai = x
- Speed of the train after the red signal = initial speed + 15 kmph
- Time taken to cover remaining distance after the red signal = half an hour

Approach:
Let the initial speed of the Sabarmati Express be v kmph. Then,
- Distance covered before the red signal = 66.666% of x = 0.66666x
- Distance remaining after the red signal = 100% - 66.666% = 33.333% of x = 0.33333x
- Time taken to cover 0.33333x distance at v kmph speed = (0.33333x)/v hours
- Time taken to cover the same distance at (v+15) kmph speed = (0.33333x)/(v+15) hours
- Total time taken = (0.66666x)/v + (0.33333x)/(v+15) + 0.5 hours

As per the problem, the train arrived at Mumbai on time, which means the total time taken is equal to the scheduled time. Therefore,
- Scheduled time = x/v

Substituting this in the above equation and solving for v, we get v = 60 kmph.

Therefore, the initial speed of the Sabarmati Express was 60 kmph.

Answer: Option B (60 kmph)
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The Sabarmati Express left Ahmedabad for Mumbai. Having travelled 300 km, which constitutes 66.666 per cent of the distance between Ahmedabad and Mumbai, the train was stopped by a red signal. Half an hour later, the track was cleared and the engine-driver, having increased the speedby 15 km per hour, arrived at Mumbai on time. Find the initial speed of the Sabarmati Express.a)50 kmphb)60 kmphc)75 kmphd)40 kmphCorrect answer is option 'B'. Can you explain this answer?
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