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Question

A train can go from Burdwan to Howrah in 6 hours and another train can go from Howrah to Burdwan in 4 hours. Both of them start at 7A.M. They will meet at

A
9.15 A.M
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B
9.22 A.M
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C
9.24 A.M
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D
9.25 A.M
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Solution

The correct option is C 9.24 A.M

Given that,
Two trains start at 7 A.M from their Starting Point

A train t1 goes from from Burdwan to Howrah in 6 Hrs

Another train t2 goes from Howrah to Burdwan in 4 Hrs

They will meet at ?

Step 1
Assume Distance between Burdwan and Howrah as a variable.

Let Distance between Burdwan and Howrah be x km

Step 2
Find the Distance Covered by the trains

Distance Covered by both the trains are equal, as both the trains are moving towards each other.

This Distance is equal to the distance between their Starting point and destination.

Distance Covered by train starting from Burdwan to Howrah = x km

Distance Covered by train starting from Burdwan to Howrah = x km

Step-3
Note the time taken by trains t1 and t2 to cover distance

Time taken by train starting from Burdwan to Howrah t1=6hrs

Time taken by train starting from Burdwan to Howrah t2=4hrs

Step-4
Find the Speed of trains t1and t2

We have,
speed=Distancetime

Speed of the train starting from Burdwan to Howrah s1=x6kmph

Speed of the train starting from Burdwan to Howrah s2=x4kmph

Step-5
Assume a variable for the time after starting time,for which both the trains are going to meet.

Let both the trains meets 'y' Hrs
Both the trains will meet at time (7+y) (1)

Step-6
Express the distance covered by both the trains in terms of Speed and time

distance=speed×time

Distance Covered by the trains = (Speed of train t1)y + (Speed of train t2)y

Step-7
Substitute Values to obtain value of y
x=(x6y+(x4yx=x(y6+y4)y(512=1y=125hrs

Step-8
Express y in Mixed Fraction.

Y=225 hrs (2)

Step-9
Express fractional part of Mixed fraction in minutes.

We have,
25hrs=25×60=24min


Step-10
Substitute in (2)

Y=225hrs = 2 Hours 24 Minutes. (3)

Step-11
Find the time at which both the trains will meet.

Substituting (3) in (1)

The time at which both the trains will meet = 7 AM + (2 Hours 24 min) = 9 Hours 24 Minutes AM


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