Question

7. A train leaves station A at 5 A.M. and reaches station B at 9 A.M. on the same day. Another train leaves Station B at 7 A.M. and reaches station A at 10.30 A.M. on the same day. The time at which the two trains cross on another is A)7.56 A.M. B)8.26 A.M. C)8 A.M. D)7.36 A.M.

Answer 1

Answer:

The time at which both the trains meet will be 7.56 a.m.

Explanation:

Given :

• A train leaves station A at 5 A.M. and reaches station B at 9 A.M. on the same day. Another train leaves Station B at 7 A.M. and reaches station A at 10.30 A.M. on the same day.

To Find :

• The time at which the two trains will cross on each other.

Solution :

$\therefore \sf{Speed}\ \infty\ \dfrac{1}{Time}$

∴  Ratio of the speeds of A and B

$\rightarrow \dfrac{7}{2/4}=7:8$

∴  A’s speed = 7x kmph (let)

B’s speed = 8x kmph

B = 7x × 4 = 28x km.

Let both trains cross each other after t hours from 7 a.m.

According to the question,

7x (t + 2) + 8x × t = 28x

$\Rightarrow$ 7t + 14 + 8t = 28

$\Rightarrow$  15t = 28 – 14 = 14

$\Rightarrow\sf{t}\ = \dfrac{14}{15}$

$\dasharrow\sf{} \bigg\lgroup\dfrac{14}{15\times60}\bigg\rgroup\ minutes$

$\Rightarrow$ 56 minutes

∴  Required time = 7 : 56 A.M.

Therefore,option A is the correct option