A train overtakes two persons walking along a railway track. The first one walks at 12.6 km/hr. The other one walks at 27 km/hr. The train takes 12.5 and 14 seconds, respectively, to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?​

Correct option is B

Given:

Speed of first person = 12.6 km/h;

Speed of second person = 27 km/h;

Time taken by train to overtake first person = 12.5 s;

Time taken to overtake second person = 14 s;

Both persons walk in the same direction as the train;

Required: Speed of the train.

Formula Used:

Length of train = (Speed of train − Speed of person) × Time

Solution:

Let speed of train be x km/h

Speed of first person = $$12.6 \times \frac{5}{18}$$​ = 3.5 m/s

Speed of second person = $$27 \times \frac{5}{18}$$​ = 7.5 m/s

Train speed = $$x \times \frac{5}{18}$$​ m/s 

Now, 

​$$\left(\frac{5x - 63}{18}\right) \times 12.5 = \left(\frac{5x - 135}{18}\right) \times 14$$​​

​$$(5x - 63) \times 12.5 = (5x - 135) \times 14$$​​

62.5x - 787.5 = 70x - 1890

1890 - 787.5 = 70x - 62.5x

1102.5 = 7.5x

x = $$\frac{1102.5}{7.5}$$​ = 147 km/h