Excluding stoppages, the average speed of a train is 120 kmph and including stoppages, it is 50 kmph. For how many minutes does the train stop per hour?a)25b)40c)35d)20Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
Average speed of train = 120 kmph
Average speed of train including stoppages = 50 kmph

To find:
Stoppage time of train per hour

Solution:
Let the distance covered by the train be D km.
Let the time taken by the train without stoppages be T1 hours.
Let the time taken by the train with stoppages be T2 hours.
Let the total stoppage time of the train be S hours.

We know that:
Average speed of train = D/T1 = 120 kmph
Average speed of train including stoppages = D/T2 = 50 kmph

From the above equations, we can write:
T1 = D/120
T2 = D/50

We also know that:
T2 = T1 + S

Substituting the above values in the equation, we get:
D/50 = D/120 + S

Simplifying the above equation, we get:
S = D(1/50 - 1/120)
S = D(12/600 - 5/600)
S = D(7/600)

Now, we need to find the value of D to calculate the stoppage time.

Let us assume that the train covers a distance of 600 km.
Then,
T1 = D/120 = 600/120 = 5 hours
T2 = D/50 = 600/50 = 12 hours

Substituting the above values in the equation, we get:
S = D(7/600) = 600(7/600) = 7 minutes

Therefore, the train stops for 7 minutes per hour.

Answer: Option (c) 35

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