**Quantitative Aptitude Trains Study Material**

**Quantitative Aptitude Trains ( Download PDF)**

This chapter is basically an extension of.the ‘Time and Distance” chapter discussed earlier, therefore, we will use here the basic concepts like Speed, Relative Speed already discussed in the earlier chapter. Here, the focus will be exclusively on problems related to trains. The variables involved are again the same—Time, Distance and Speed. •Assumptions : For all purposes, unless otherwise specifically mentioned, we will assume that the speed at which the train(s) covers the distance or performs the journey remains constant over the journey which we call the average speed. The size of the person, telegraph post, pole etc. is negligible in comparison to the length of the train or the platform.

**Assumptions** : For all purposes, unless otherwise spe-cifically mentioned, we will assume that the speed at which the train(s) covers the distance or performs the journey re-mains constant over the journey which we call the average speed. The size of the person, telegraph post, pole etc. is negligible in comparison to the length of the train or the platform

**Important General Cases** :

(i) Time (T) taken by a train x metres long to cross a stationary person or pole or signal post is equal to the time taken by the train to cover the distance x metres (equal to its own length) with its own speed (v).

So, t =x/v

**Ex. 1. (i) How much time will a train 300 metres long running at 54 km/hr take to pass a stationary pole?**

Sol. Length of the train= 300 m

Speed of the train= 54 km/hr = 54x (5/18) m/ s = 15m/s

Time taken by the train to pass the pole

= 300/15 = 20 seconds

(ii) Time taken by a train x metres long to cross a sta¬tionary objects (like platform, bridge, tunnel, standing train etc.) of length y metres equals the time taken by the train to cover a total distance (x+y) metres at its own speed (v).

t= x+y/v

Note: In every case the units of various variables must made consistent before performing calculation

**Ex 2. Find the time taken by a 100 m long train running at 36 km/hr to cross a bridge 300 m long.**

Sol. Total length (x + y)= (100 + 300) m = 400 m Speed of the train (v)= 36 km/hr

= 36×5/18 m/s = 10m/s

Time taken= x+y/v = 400/10 = 40 seconds

(iii) (a) A train x metres long running at speed v passes an object of length y metres moving at speed u in the same direction:

Sol. The train will be able to cross the object only if v is greater than u

Relative speed of the train (with respect to the object) = (v-u)

Total distance to be covered = (x + y) metres

Time taken by the train to cross the moving object = x+y/v-u

Note: The moving object may be another train, carriage etc.

If the object is man, or any other thing whose size is negligible in comparison to the length of the train, then we put

y = 0. In that case the above relationship changes to x/ v-u

**3. Two trains 130 m and 120 m in length are running in the same direction at 70 km/hr and 52 km/hr respectively. In what time will they be clear of each other from the moment they meet?**

Total distance to be covered = x + y = (130+ 120) m = 250m

Relative speed of the trains

= (70-52) km/hr =18 km/hr = 18x-5/18 m/s = 5m/s

Time taken = 250/5 = 50 seconds

If two trains A and B start simultaneously from stations P and Q and move towards each other at speed S, and S2 km/hr respectively. At the point where they meet, one train has covered x km more than the other. Then the distance between P and Q is (s1+s2/s1-s2)

Two trains A and B start simultaneously from stations P and Q, x km apart and move towards each other. They meet after time 1 hours. If the difference in speeds of the two trains is S km/hr, the speeds of the two trains would be:

If a train covers a certain distance non-stop, its average speed is S1 km/hr, but when it covers the same distance with stoppages its average speed is reduced to S2 km/hr.

then on an average the train stops for (S1-S2/S1) hpur for every hour travelled.

Two trains of lengths l1 and l2 metres run on parallel tracks. When running in the same direction, the faster train passes the slower one in f, seconds. But when they are running in opposite directions at same speeds as earlier, they cross each other completely in t2 seconds. The speeds of the

**Quantitative Aptitude Trains ( Download PDF)**