Question

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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Answer 1

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.

Answer 2

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.