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AFCAT Model Paper 5

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Question : 56 of 100

Marks: +1, -0

A train can travel 25% faster than a car. Both start from a point A at the same time and reach at a point B 360 km away from A at the same time. On the way, however, the train lost about 1 hour 48 minutes while stopping at the stations. Find the speed of the train and the car.

50 km/hour, 40 km/hour
60 km/hour, 48 km/hour
75 km/hour, 60 km/hour
45 km/hour, 36 km/hour

Solution:

Formula used:

Speed = distance/time

Calculation:

Let the speed of car be X km/hour

So, the speed of train

= X \times \frac{5}{4} = \frac{5X}{4}

km/hour

Time taken by car to cover 360 km =

\frac{360}{X}

hour

And the time taken by train to cover 360 km

= \frac{360}{\frac{5X}{4}} = \frac{288}{X}

Time taken by train while stopping

= 1 + \frac{48}{60} = \frac{9}{5}

hour

So,

\frac{360}{X} - \frac{288}{X} = \frac{9}{5}

\Rightarrow \frac{72}{X} = \frac{9}{5}

⇒ X = 40 km/hour

∴ The speed of car = 40 km/hr and the speed of train $= \frac{5}{4} \times 40 = 50$ km/hr.

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