Today, We are going to take a test on Problems based on Train.

Before you take the test read these posts to be comfortable.

Shortcuts and Tips for Train Problems

**Important Formulae
**

1, *km/hr to m/s conversion:*

* a* km/hr =m/s.

2, *m/s to km/hr conversion:*

*a* m/s =km/hr.

3, **Formulas for finding Speed, Time and Distance**

(i) *Speed, Time and Distance:*

Speed = , Time = , Distance = (Speed x Time).

(ii) *km/hr to m/sec conversion:*

*x* km/hr =m/sec.

(iii) *m/sec to km/hr conversion:*

*x* m/sec =km/hr.

(iv) If the ratio of the speeds of A and B is *a* : *b*, then the ratio of the the times taken by then to cover the same distance is or *b* : *a*.

(v) Suppose a man covers a certain distance at *x* km/hr and an equal distance at *y* km/hr. Then,the average speed during the whole journey is km/hr.

4, Time taken by a train of length *l* metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover *l* metres.

5, Time taken by a train of length *l* metres to pass a stationery object of length *b* metres is the time taken by the train to cover (*l* + *b*) metres.

6, Suppose two trains or two objects bodies are moving in the same direction at *u* m/s and *v* m/s, where *u* > *v*, then their relative speed is = (*u* – *v*) m/s.

7, Suppose two trains or two objects bodies are moving in opposite directions at *u* m/s and *v* m/s, then their relative speed is = (*u* + *v*) m/s.

8, If two trains of length *a* metres and *b* metres are moving in opposite directions at *u* m/s and *v* m/s, then:

The time taken by the trains to cross each other = sec.

9, If two trains of length *a* metres and *b* metres are moving in the same direction at *u* m/s and *v* m/s, then:

The time taken by the faster train to cross the slower train =sec.

10, If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take *a* and *b* sec in reaching B and A respectively, then:

(A’s speed) : (B’s speed) = .