question_answer

A and B are two stations 1000 km apart. A train starts from A and moves towards B at 40 km/h. Another train starts from B at the same time and moves towards A at 60 km/h. How far from A will they cross each other?

A) 350 km             

B) 400 km

C) 525 km

D) 300 km

E) None of these

Correct Answer: C

Solution :

Let the two trains cross each other at C.

Let the train A reach the point C after x h.

and the train B reach the point C after y h.

Then,    \[4x+60y=1000\]                       ... (i)

and       \[\frac{x+y}{2}=\frac{1000}{60+40}=\frac{1000}{100}=10\]

\[\Rightarrow \]               \[x+y=20\]                    (ii)

Solving for x and y,

\[x=10\]and \[y=10\]

\[\therefore \]Train from A will cross B after \[x\times 40=400\,\,km\]