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

CAT 2020 – The CAT QA section has grown increasingly difficult since 2015. In order to tackle the tougher CAT Level QA questions for the CAT Exam, it is important to understand the basics of CAT. To obtain a great CAT score, make use of MBAP Free Study material with detailed solutions and video explanations. Check out MBAP free Mock test to take these questions in a test format for free.

You may also find remaining question solution of CAT 2020, slot 1 by searching the question in the search bar. The question below is from previous year CAT question from CAT 2020 exam comes from CAT Time Speed Distance: A train travelled at one-thirds of its usual speed Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2020 - Slot 1 - Quantitative Aptitude - TSD - Question 4 - A train travelled at one-thirds of its usual speed

Q. 4: 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. 58
2. 67
3. 50
4. 61

Correct Answer: 67

Let’s take speed of the train to be x and the time taken be t

Since speed is reduced to 1/3 rd,

New speed = x/3

Since the speed is one-third, time taken will be tripled. T = 3t

This 3t is after the scheduled time, So extra 2t = 30 mintues

t = 15 minutes

Train travels at x km/hr takes 15 minutes and

Train travels at x/3 km/hr takes 45 minutes

So, the train usually takes 15 minutes to cover the distance.

It travels 5 minutes at the usual speed. That is, it travels 1/3 rd of the time at the usual speed. So it covers 1/3 rd of the distance in 5 minutes.

To reach it’s destination in the on time, the train has to travel the remaining 2/3 rds of the distance in 10 minutes. Since the train halts for 4 minutes, it should now cover the 2/3 rds of the distance in 6 (10 – 4) minutes.

In other words, the train has to cover the same distance in 6/10 th of the usual time.

In order to do so, the speed must be 10/6 ths of the usual speed. Or the increased speed will be 4/6 ths or 2/3 rds of the usual speed. Which is an increase of 66.66% or nearly 67%.

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