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View Answer
Shortcut:
The distance between two stations, X and Y is D km. A train starts from X and moves towards Y at an average speed of a km/hr. If an another train starts from Y, t hours earlier than the train at X, and moves towards X at an average speed of b km/hr, then the distance from X where the two trains will meet, is
(D + tb) x
a
/
a + b
km.
Here, D = 300, a = 10, b = 30, t = 3.50 pm − 3.10 pm = 40 minutes or
40
/
60
or
2
/
3
hours
Using these values in the shortcut, we get:
Required distance = (300 +
2
/
3
x 30) x
10
/
10 + 30
= (300 + 2 x 10) x
10
/
40
= (300 − 20) x
1
/
4
= 320 x
1
/
4
= 80
Hence, the required distance is 80 km.
Time taken by X to cover 80 km =
80
/
10
= 8 hours
Hence, train will meet after 80 km from Delhi at 11:10 pm
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