Question

10. If a train runs at 40 kmph it reaches its destination late by 11 minutes. But if it runs at 50 kmph it is late by 5 minutes only. Find the distance to be covered by the train.

The answer should come as 20km


Please answer correct​

Answer 1

Let the distance covered by the train be x km.

↣Time delay when speed is 40 kmph =

11 minutes.

↣Time delay when speed is 50 kmph =

5 minutes.

↦The difference in time for different speeds =

11 – 5

↦6 minutes.

↣$\rm \frac{6}{60} = \frac{1}{10} \: hours$

We know that:-

$\rm\frac{distance}{time}$

∴Time:-

$\rm \frac{distance}{speed}$

Attording to given condition:-

↣$\rm \frac{x}{40} - \frac{x}{50} = \frac{1}{10}$

↣$\rm \frac{5x - 4x}{200} = \frac{1}{10}$

(LCM of 40 and 50 is 200)

↣$\rm\frac{x}{200} = \frac{1}{10}$

↣$\rm \frac{x}{200} \times 200 = \frac{1}{10} \times 200$

(Multiplying both sides by 200)

↣$\rm{x = 20}$

∴The distance covered by the train is 20 km

hope it helps :)