Problems on Trains, Poles and Platforms are my favourite!

Basically, these problems use the same rules that we saw in the chapter of ‘Time, Distance and Speed.’

In competitive exams you will be asked various kinds of questions like

•Find the relative speed of two trains A and B running in the same direction

•Find the relative speed of two trains A and B running in opposite direction

•How much time will a train take to pass a person or a pole

•How much time will a train take to pass an entire platform

There are handy short-cuts to solve all such type of questions. Students often complain to me that it becomes a little tedious to memorize all these short-cut formulas. However, my only answer to them is that since they are appearing for competitive exams (with lakhs of other students), they must be fully prepared. There should be no compromise on preparations.

Also, for those of you who are having a generic problem in remembering things, I strongly recommend you read my book ‘Memory Power.’ It is available across the world (online as well as offline).

The book is priced modestly and it will teach you some fantastic techniques to improve your memory.

(Search for the book MEMORY POWER by Dhaval Bathia on Google)

**Q1) A train runs non-stop from New York to Boston at the speed of 100 km/hr. In its second journey, it stops at various places in between and covers the same distance at an average speed of 80 km/hr. Find out the total halt time of the train.**

Ans: I will give you an easy formula to find the total halt time of the train.

Direct Formula Number 1

Halt Time = Non-Stop Speed – Speed with Stops

Non-Stop Speed

100 – 80

20 = 1 hour = 12 minutes

100 100 5

Hence the train stopped for 12 minutes in the journey.

Another faster method to solve such questions is to note that the speed of the train has reduced by 20% (20 km on 100 km) and 20% of 1 hour is one-fifth and one-fifth of sixty minutes is 12 minutes.

In professional exams, you should not waste your time in writing down the entire question with a pen on your answer paper, instead, all such calculations must be done mentally at lightning speed!

**Q2) Two trains leave Moscow city and Kazan city simultaneously. The speed of the first train is 90 km/hr and the speed of the second train is 110 km/ hr. When they meet, the faster train has travelled 200 kms more than the slower train. Please find the distance between the two cities.**

Ans: The question may appear complicated at first sight. There is no need to take stress. Just focus on the standard basics that you know.

Here we have to find the distance for which we need

both speed and time.

Time: We know one train is faster than the other by 20 km/hr (110 – 90) and the faster train has travelled 200 kms more. So the trains have run for 200/20 = 10 hours.

So, time is 10 hours

Speed: Since the trains are travelling in opposite directions, the combined speed is the speed of train A + speed of Train B = 110 + 90 = 200 km/hr

So, speed is 200 km/hr Distance = Speed × Time = 200 × 10 = 2000 kms.

The distance between Moscow and Kazan is 2000 kms.

**Q3) Two trains of length 110 meters and 130 meters run daily from Los Angeles to Las Vegas. When running in the same direction the faster train passes the slower train in 30 seconds. But when running in the opposite direction, the faster train passes the slower train in 15 seconds. Find the speed of the faster train as well as the slower train.**

Ans: We will solve this problem twice. First we will solve it with the algebraic method and then I will give you a direct formula to solve this question.

Method 1: Algebra

Let the speeds of the trains be P and Q

When trains are moving in the same direction, their relative speed is (p – q)m/s

When they are moving in opposite directions, their relative speed is (p + q)m/s

So, p – q = Length of Train 1 + Length of Train 2

= 30

And,

= 240 = 8

30

p + q = Length of Train 1+Length of Train 2

=15

= 240 = 16

= 15

We know that p – q is 8 and p + q is 16. Therefore 2P = 24 and P = 12

On substituting, we get P = 12 and Q = 4 The speeds of the train are 12 m/s and 4 m/s Now let us try to solve this same question by a direct formula

Direct Formula Number 2

Speed of 1st Train = Avg. length of Two Trains

Same Directions Time Opposite Directions Time

Speed of 2nd Train = Avg. length of Two Trains

Same Directions Time Opposite Directions Time

Note that the first equation has a positive sign and the

second equation has a negative sign.

(We ignore minus sign as speed is never negative)

Hence, we know that the speeds of the two trains are 12

m/s and 4 m/s

I personally find the second formula to be better as it is etched in my mind. You may choose to solve by any of the two approaches that suit you.

**Q4) John is walking at the speed of 0.5 m/s and Joseph is walking a few miles ahead at the speed of 1 m/s. A train, moving in the same direction overtakes them in 10 seconds and 12 seconds respectively. Find the train’s length.**

Ans: Dear Readers, please note that I could have chosen very easy problems in the book which you could have solved instantly. It would have boosted your ego and made you feel nice. In return you would have showered praises on my book too. However, as a teacher this is not my intention. My aim is to raise the level of your thinking and solving to very high levels so that it helps in sharpening your intellect.

Often we are asked such questions where we do not know where to begin. As always, let me give you a direct formula that will help you to solve such questions

Direct Formula

Let the time taken to Overtake the two men be OT1 and OT2 respectively

Train’s Length =

Difference in Speed of Two Men*OT1*OT2

(OT 2 – OT1)

Train’s Length =

(1- 0.5)*10*12

(12 – 10)

= (0.5)*120 = 60 = **30 meters**

Ans: The length of the train is 30 meters. So easy, isn’t it?

**Q5)An express train passes a railway platform which is 50 metres long in 30 seconds. Further ahead, it passes a signal post in 20 seconds. What is the length of the railway platform?**

Ans: As always, we will try to solve this question by two methods. In the first method, I will show you the cumbersome and lengthy method of calculation and then in the second method I will give you a direct short-cut formula to crack such a question.

Presume that the length of the train is M metres. On equating the respective speeds, we have,

M = M + 50 20 30

# Method 1

30M = 20M + 1000

10M = 1000 and hence M = 100 meters.

So, we get that the length of the train is 100 meters.

Now let me give you a direct formula to find the length of the train

Direct Formula

Length of Train =

Platform Length × Pole Passing Time

Difference in time to cross Platform and Pole

From the above direct formula, we instantly know

Length of Train = 50 × 20 = 1000 =100 meters.

30-20 10

So you can see that you got the same answer by using the direct formula, albeit in a much lesser time.

So with this we come to the end of this chapter.

Please use these short-cuts and popularize them with anyone in your family or friend’s circle who is giving any kind of competitive or entrance exams. It will give them a huge edge in their preparations.