Quantitative Aptitude – TSD – A train travelled at one-thirds of its usual speed

Slot – 1 – Quantitative Aptitude – TSD – A train travelled at one-thirds of its usual speed

Q. 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?

1. 50
2. 61
3. 67
4. 58

Answer: 67

Solutions:
Let the original speed = v and actual time = t
Then,
V1/v2 = t2/t1
V1/(v1/3) = (t + 30)/t
3t = t + 30
t = 15 minutes
now , in its return journey , the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency.
So now the train need to cover 10 minutes journey (15 -5) in (10 -4 = 6) minutes
Thus new speed = 10v/6 = 1.666 v
Increase in speed = (1.666v –v)/v*100 = 66.66% or 67%

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