QUESTION

CSAT

Easy

Maths

Prelims 2017

A freight train left Delhi for Mumbai at an average speed of 4040 km/hr. Two hours later, an express train left Delhi for Mumbai, following the freight train on a parallel track at an average speed of 6060 km/hr. How far from Delhi would the express train meet the freight train?

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Explanation

Let the time taken by the express train to meet the freight train be tt hours.

The freight train travels for (t+2)(t + 2) hours, since it left 2 hours earlier than the express train. Distance covered by the freight train = Speed × Time = 40×(t+2)=40(t+2)40 \times (t + 2) = 40(t + 2) Distance covered by the express train = Speed × Time = 60×t=60t60 \times t = 60t Since both trains meet at the same point, their distances are equal: 40(t+2)=60t40(t + 2) = 60t Expand the equation: 40t+80=60t40t + 80 = 60t Solve for tt: 80=60t40t80 = 60t - 40t 80=20t80 = 20t t=4t = 4 Distance from Delhi to the meeting point (distance covered by the express train): Distance = 60×4=24060 \times 4 = 240 km Answer: C. 240 km

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