IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 22 : A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.

1. 3 AM the next day
2. 4 AM the next day
3. 8 AM the next day
4. 11 PM the same day

Video Explanation

Explanatory Answer

The first train starts and after 2 hours the second train starts from the same place. They both meet at 8PM
So train A has traveled for 8 hours and train B has traveled for 6 hours.
The ratio of their time taken is 4 : 3
Which means the ratio of their speeds 3 : 4
Now it is given that the sum of the speeds is 140.
Let the speed be 3x and 4x then the sum of the speed will be 7x = 140 or x = 20
So the speeds are 60 and 80 kmph
The relative speed between the two trains is 80 - 60 = 20 kmph,
So the faster train catches up 20 km every hour.

In the scenario when the faster train starts 5 hour later than the slower train the first train has a head start of 5 * 60 = 300km.
To cover the 300km, the faster train would require \(\frac{300}{20}\) = 15 hours as the faster train catches up by 20 km every hour.
So 15 hours after 5 PM is 8AM in the morning when the two trains meet.

The answer is '8 AM the next day'

Choice C is the correct answer.