CAT level questions on time and distance

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CAT level questions on time and distance
A detailed blog on CAT level questions on time and distance

Quantitative aptitude is one of the most scoring sections in CAT. Aspirants can take free CAT mock tests to check where they stand. Solving previous year papers of CAT will help aspirants understand the level of difficulty of questions. In this blog, let us look at some CAT level questions on time and distance.

Time, speed, and distance is one of the simplest topics tested in CAT. Solved Time speed Distance CAT Questions will help you to learn more. Hence, aspirants must try to maximise their scores in these topics before moving on to esoteric concepts.

Basic terms that will be useful in solving CAT level questions for time-speed-distance are relative speed and effective speed. Aspirants can try online preparation for CAT to assist them in their preparation.

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CAT level questions on time and distance:

Time * speed = distance.
Students can solve most of the CAT level questions on time and distance just by remembering this fundamental relationship.

Question 1:

A and B start at the same time from cities P and Q respectively that are 300 km apart and move towards each other. They meet at a point 120 km from P. At what time will A reach Q provided that both A and B start at 3 AM and B reaches P at 1 PM?

Since they start at the same time, the ratio of distances covered will be equal to the ratio of the speeds. Let us assume A’s speed to be ‘a’ and B’s speed to be ‘b’.

Hence, a/b = 120/(300-120)
a/b = 120/180
3a = 2b
b =1.5a.

A will cover 300 Km in 300/a hours.
B will cover 300 km in 300/1.5a = 200/a hours.

It is given that 200/a = 10 hours (3 AM to 1 PM)
=> a = 20
Hence, A will reach 300/20 = 15 hours after 3 AM.
Hence, A will reach Q at 6 PM.

Question 2:

Boats A and B travel at 20 kph and 30 kph. They start at 1 PM towards each other and collide at 2:30 PM. What will be the distance between the 2 boats just a minute before their collision provided that the distance between the two boats was 70 km at 1:06 PM.

This question is based on a previous year CAT question. The question is elementary but confuses the aspirants by providing superfluous data.

We can rephrase the question as ‘Two boats travelling at speeds 20 kph and 30 kph are travelling towards each other. What will be the distance travelled by them in a minute?’

Since the boats are travelling towards each other, they will cover 20+30 = 50 km in an hour. In a minute, they will cover 50/60 = 5/6 km.

Question 3:

A, B, and C run a race of 1000 m. A beats B by 5 seconds and C by 500 metres. B and C decide to run a 5000m race. C gives up mid way. For how much time must B run after C gives up to complete the race.

Let the speeds of A, B, and C be a, b, and c.
We know that (1000/a) = (1000/b) – 5 ——————(1)
Also, 1000/a = 500/c
=> a = 2c —————–(2)

Substituting a = 2c in (1), we get,
500/c = 1000/b – 5
1000/b = 500/c + 5. —————-(3).

C gives up midway in the 5000 m race. This means that C gives up after running 2500m.

Multiplying (3) by 5, we get, 5000/b = 2500/c + 25.

The above equation means that 25 seconds would have elapsed after C had run 2500m by the time B completes running 5000m. Hence, 25 seconds is the right answer.

Question 4:

The following question is based on a previous CAT question. This question will definitely feature among one of the most beautiful CAT level questions on time and distance.

A Cat is standing inside a tunnel at a point 3/8 th the length of the tunnel from the entrance. The cat hears a train whistling. The Cat will manage to barely save itself if it decides to run either towards the entrance of the tunnel or the exit. What is the ratio of speeds of the train and the Cat?

Let us assume the length of the tunnel to be 8 km for ease of solving.

We do not know where the train is. But, we know that if the Cat runs towards the entrance, it barely manages to save itself. Hence, by the time Cat runs 3 km, the train reaches the entrance of the tunnel.

Now, let us assume that the Cat runs towards the exit of the tunnel.
The cat is standing at a point 3 km from the entrance of the tunnel. By the time the cat runs 3 km, the train would have reached the entrance of the tunnel. Hence, by the time the train reaches the entrance, the Cat will be at a point 6 km from the entrance of the tunnel and 2 km from the exit of the tunnel.

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We hope that this article on CAT level questions on time and distance would have given you some idea about the different types of questions that can appear in the exam. Try reading our other helpful blogs data interpretation basics for CAT and FAQs on CAT mocks.We know that the cat barely manages to save itself even if it runs towards the exit of the tunnel. Hence, by the time the cat covers 2 km (towards the exit), the train must have covered 8 km (the entire length of the tunnel). Hence, the ratio of speeds of the train to that of the cat is 8:2 = 4:1.

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