Question

Two express trains A and B simultaneously started on two tracks from Varanasi to

Delhi, which are 390 km apart. The ratio of the speed of express A and B is 6: 7. After

how many kilometers would express B exchange speed with express A, so that both

trains reach their destinations simultaneously?

(a) 150 km

(b) 190 km

(c) 210 km

(d) 250 km

Answer 1

Answer:520km

Step-by-step explanation:

Let D be the Distance between Varanasi & Delhi

Train A & Train B start from Varanasi at the same time with different speeds in the ratio of 6:7

That is, Speed of train A = 6 units & Speed of train B = 7 units

Let t be the time from start, at which Trains A & B exchange their speeds.

Also Let T be the time from start, at which both the trains reach Delhi together.

In the First leg of Journey, Let DA and DB be the distances travelled by trains A & B in time t.

DA = 6t & DB = 7t ……………….. (1)

In the second part of journey, the trains exchange their speeds and the respective distances travelled by trains A & B are given by:

D - DA = 7(T -t) & D - DB = 6(T -t)

On substituting the values of DA and DB from Eqn. (1), we get

D - 6t = 7(T -t) ………………………. (2)

D - 7t = 6(T -t) ………………………. (3)

By subtracting Eqn (3) from (2) we get

t = (T -t) . That is, t = T/2 (Both parts of the journey are done in equal time t, by both the trains A & B)

So, Train B first travels distance of 7t and in the second half travels 6t

It follows that, Total distance between Varanasi and Delhi, D = 7t + 6t = 13t

So at 7/13 th of the distance (bet. the two stations) the Train B exchanges its speed (with that of train A).

To illustrate this with an example, let the distance D be 520 km, bet, Var. & Del.

Let the starting speeds of trains A & B be 60 kmph and 70 kmph

So D = 70t + 60t = 130t = 520 km. ie, t = 520/130 = 4 h

So in the first 4 hours trains A & B travel 240 and 280 km respectively

in the next 4 hours they travel 280 and 240 km respectively and hence both reach Delhi together after 8 hours from start

So the train B exchanges speed at 280 km which is nothing but 7/13 th of the Distance of 520 km.

Answer 2

Answer:

520 km

Step-by-step explanation: Let D be the Distance between Varanasi & Delhi

Train A & Train B start from Varanasi at the same time with different speeds in the ratio of 6:7

That is, Speed of train A = 6 units & Speed of train B = 7 units

Let t be the time from start, at which Trains A & B exchange their speeds.

Also Let T be the time from start, at which both the trains reach Delhi together.

In the First leg of Journey, Let DA and DB be the distances travelled by trains A & B in time t.

DA = 6t & DB = 7t ……………