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Question

A train normally covers a certain distance at a speed of 60 km/hr. However, if it were to halt for a fixed time interval in each hour its average speed reduced to 50 km/hr. What is the time interval for which the train halt in each hour?

A
10 minutes
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B
20 minutes
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C
6 minutes
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D
12 minutes
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Solution

The correct option is A 10 minutes
This question can be solved by alligation.
Speed when moving = 60 km/h
Speed when at rest = 0 km/h
Average speed = 50 km/h (Given)

Hence, time ratio = 5 : 1.
In one hour, train moved for 50 min and rested for 10 min.

Alternate Approach:
For this type question, take the LCM of speeds and assume the LCM as the distance.
then the time taken @ speed of 60km/hr =30060= 5 hrs
again the time taken @ speed of 50 km/hr =30050 = 6hrs
Thus we see that in place of 5 hrs train takes 6 hours. It means the train takes 1 hour extra and this one hour is stopping period in the total time of 6 hours. Thus in 6 hours, train halts for 1 hour. So in 1 hour, the train will stop for 16 hours or 10 minutes.

Alternatively: (short cut)
Halting (or stopping) time =(1slower speedfaster speed)hours
=15060=1060=16hours
= 10 minutes
( 1 hour = 60 minutes)

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