Time, Speed and Distance Question 9 - CAT 2020
A train travelled at one-third 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:
Step-by-Step Explanation
Determine the scheduled travel time:
When speed drops to 1/3, the time taken increases to 3 times the usual time (3t).
Time Delay = 3t − t = 2t = 30 minutes ⟹ t = 15 minutes
The total scheduled trip duration is 15 minutes.
Analyze the return journey:
First 5 minutes: Travels at usual speed s, covering:
5/15 = 1/3
of the total route distance.
Next 4 minutes: Stopped due to an emergency.
Total time elapsed = 5 + 4 = 9 minutes
Remaining time to stay on schedule = 15 − 9 = 6 minutes
Remaining distance to cover = 1 − 1/3 = 2/3 of the route
Calculate the required speed scaling:
At her usual speed, covering this remaining 2/3 of the distance would take 15 − 5 = 10 minutes. To finish this remaining distance on time, she must complete a 10-minute journey in just 6 minutes.
Time Ratio (Usual : New) = 10 : 6 = 5 : 3
Required Speed Ratio (Usual : New) = 3 : 5
Percentage Increase = (5 − 3)/3 × 100%
= 2/3 × 100% ≈ 66.67% ≈ 67%
Correct Option: C
💡 FundaMakers Tip:
Avoid calculating absolute distances or speeds! Work entirely in ratios. Recognizing that a 10-minute segment must be completed in 6 minutes tells you that the speed must be scaled up by the inverse ratio (10/6 = 5/3). An increase from 3 to 5 is a 2/3 increase, which translates directly to 67%.