A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to
Explanation:
Since the train travelled at 1/3rd of its speed, it will take thrice the usual time.
Hence, if the normal time taken for train is t minutes, now it will take 3t minutes.
∴ 3t – t = 30
⇒ t = 15 minutes.
While coming back train travels at usual speed for 5 minutes and then takes 4 minutes break.
∴ If the train has to come back at scheduled time, it needs to cover the remaining distance in (15 – 5 – 4 =) 6 minutes. Train usually takes 10 minutes to travel this distance.
∴ The time reduced to 6/10 = 3/5th hence speed should become 5/3 times.
∴ % increase = 53-11 × 100 = 66.66% ≈ 67%
Hence, option (c).
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