CAT 2017 Question Paper | Quants Slot 1

CAT Speed time distance is one of the most commonly tested topics in CAT exam. Questions from speed, time and distance have appeared consistently in CAT Question Paper. One can usually expect 3-4 questions from this idea in the CAT exam. In a hurry? Have a go at this problem before you leave. Maybe this problem would help you to calculate how late you are going to be. Make use of 2IIM'S Free CAT Question Bank provided with detailed solutions and Video explanations to obtain a wonderful CAT score.

Question 4 : A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is: [TITA]

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Speed Time Distance

Given that a man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed.
If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure.
⟹ $\frac{d}{12}$ is one time taken and $\frac{d}{15}$ is another time taken.
The difference between these two times is 20 minutes
We have to find the distance (in km) from his home to the railway station.
20 mins is $\frac{1}{3}$^rd of an hour.
⟹ $\frac{d}{12}$ = $\frac{d}{15}$ + $\frac{1}{3}$
⟹ $\frac{d}{12}$ - $\frac{d}{15}$ = $\frac{1}{3}$
⟹ $\frac{5d - 4d}{60}$ = $\frac{1}{3}$
⟹ $\frac{d}{60}$ = $\frac{1}{3}$
⟹ d = 20 km
The distance (in km) from his home to the railway station is 20 km.
Important point to remember is that we don’t need to take the actual time here, we can take that difference of 10 minutes before and 10 minutes after which is equal to 20 minutes i.e. $\frac{1}{3}$^rd of an hour.

The question is "A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is: [TITA]"

Hence, the answer is 20 km

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