Question

The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
A) 10 a.m.
B) 10:30 a.m.
C) 11 a.m.
D) 11:30 a.m.

Answer 1

Hint:
First, we will find the distance travelled by the train in 1 hour. Then, we will find the distance between two trains at 9 a.m. After that, we will find the relative speed of the two trains and using it we can find the meeting point of two trains.

Complete step by step solution:
Here, it is given that the distance between two cities A and B is 330 km.
$\because $A train starts from ‘A’ at 8 a.m. and travels towards ‘B’ at 60 km/hr.
Another train starts from ‘B’ at 9 a.m. and travels towards ‘A’ at 75 km/hr.
So, at what time do they meet?
Distance travelled by first train in one hour $ = 60 \times 1 = 60km$
$\therefore $Distance between two trains at 9 a.m. $ = 330 - 60 = 270km$
Now, relative speed of two trains $ = 60 + 75 = 135km/hr$
$\therefore $Time of meet of two train $ = \dfrac{{270}}{{135}} = 2hrs$
 Both the trains will meet at $9 + 2 = 11a.m.$

Hence, both the train will meet at $11a.m.$

Note:
In other way the above question is represented as:

T $ = \dfrac{{270}}{{60 + 75}}$
$\therefore T = 2hrs$
So, time t which they meet =11:00a.m.