Q. 31. A train travelling at 65km/hr leaves Bombay at 10 a.m., and another train travelling at 75km/hr in the same direction leaves Bombay at:12 Noon: How many km: from Bombay will they be together? (1) 1050 km (2) 1000 km (3) 975 km 925 km Hi
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Answers
Given :-
▪ Train A is travelling at s₁ = 65 km/h leaves Bombay at 10 am , and another train B travelling at s₂ = 75 km/h leaves Bombay at 12 am
To Find :-
▪ How many km from Bombay will they be together?
Solution :-
It is clear that they leave the station with a 2 hour gap. Let us find the relative velocity of the trains.
⇒ Rel. Velocity = 75 - 65
⇒ Rel. Velocity = 10 km/h
Now, Let us find the distance travelled by the train A before train B left, which is equal to the distance travelled in 2 hours by train A.
⇒ Distance travelled, d₁ = 65 × 2
⇒ d₁ = 130 km
Now, Let us find the time after which train B will cover this distance with respect to train A.
⇒ Time taken = 130 / 10
⇒ Time taken = 13 hours
Now, They would meet each after 13 hours as train B leaves Bombay.
So, Distance at which they will meet each other,
⇒ D = d₁ + 65 × 13
⇒ D = 130 + 845
⇒ D = 975 km
Hence, The will meet each other at a distance of 975 Km from Bombay.
So, Option (3) is correct.
The train starting at 9 a.m. has travelled by 2 p.m. a distance of (5×25)km. i.e., 125 km.
Relative speed of two trains =(35−25); i.e., 10 km. per hour.
The second train shall meet the first train in
10
125
; i.e., 12.5 hrs.
Distance from Aligarh=12.5×35 km=437.5 km.