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Maths ki Class: Problem on Trains

Trains is very common topic found in almost all exams like SSC CGL, SSCL MTS and SSC-CPO as well as various banking sector exams.

Conversion Formula:

2. m/s to km/hr conversion:

Formulas for finding Speed, Time and Distance

3. 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.

4. 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.

5. 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.

6. 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.

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

8. 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:

9. 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) 

Solved Example

X and Y are two stations 390 km apart. M train starts from X at 4 p.m. and travels towards Y at 65 km/h. Another train N starts from Y at 5 p.m. and travels towards X at 35 km/h. At what time do they meet?

Solution: Distance b/w X & Y = 390km

Speed of train M= 65 km/h

Speed of train N= 35 km/h

Total distance need to cover = 390 km

Hence, Total distance, Distance cover by M + Distance covered by N =390 km------- (1)

Let us assume M takes T time, starting 4 p.m.

Now, Distance covered by M = Speed of M × Time taken ⇒ 65t ------ (2)

So if M takes t time then N will take (t-1), because M started 1 hour before.

Distance covered by N = Speed of M × Time taken ⇒ 35(t-1) ----- (3)

Put in equation (1)

65t + 35(t-1) = 390

65t + 35t – 35 = 390

100t = 425

t = 4.25 hours or 4hrs 15 minutes

So they will meet after 4hrs 15 min, at 6:15 PM.

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