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Distance to Railway Station

CAT 2017 Slot 1 · Quantitative Ability · Easy · Speed, Time and Distance

This is an easy Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Speed, Time and Distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A man leaves his home and walks at a speed of 12 km/h12\text{ km/h}, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km/h15\text{ km/h}, 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:

Answer

20

Explanation

Let distance be D kmD\text{ km}. Time difference between two speeds = 10−(−10)=20 minutes=13 hours10 - (-10) = 20\text{ minutes} = \frac{1}{3}\text{ hours}. D12−D15=13\frac{D}{12} - \frac{D}{15} = \frac{1}{3} 5D−4D60=13  ⟹  D60=13  ⟹  D=20 km\frac{5D - 4D}{60} = \frac{1}{3} \implies \frac{D}{60} = \frac{1}{3} \implies D = 20\text{ km}.

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