Train formulas and practice sums for competitive exams

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Introduction

In this competitive world, many people aspire to achieve greatness. For success, many aspirants are preparing for competitive exams, their main goal is to pass that exam and live a good life. If this is your goal too, Nithra Jobs can help you get there faster with simple train formula sums and practice questions. Here we learn the basic Train formula sums. Learn the sums quickly with the help of these Train formulas provided by Nithra Jobs.

Trains

Formulas:

km/hr to m/s conversion:

a km/hr = (a * 5/18) m/s

m/s to km/hr conversion:

a m/s = (a * 18/5) km/hr

Formulas for finding Speed, Time and Distance

Speed = Distance / Time

Time = Distance / Speed

Distance = Speed * Time

If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by then to cover the same distance is

1 / a : 1 / b = b : a

• 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

(2xy / x+y) km/hr

• 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.

• 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.

• 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.

• 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.

• 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 = (a + b) / (u + v) sec.

• 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 = (a + b) / (u - v) sec.

• 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) = (√b : √a)

Solved Problems

1. How many seconds will a 600-metre-long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 83 km/hr?

Answer: 27 sec.

Explanation:

Speed of the train relative to man = ( 83 - 3 ) km/hr

= 80 km/hr

= [ 80 * ( 5 / 18) ] m/sec

= ( 400 / 18 ) m/sec.

Time = Distance / Speed

Time taken to pass the man

= [ 600 * ( 18 / 400 ) ] sec

= ( 6 * 18 ) / 4

= ( 108 / 4 )

= 27 sec

It will take 27 seconds.

2. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 55 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Answer: 16.36 sec

Explanation:

Relative speed = (45 + 55) km/hr

= [ 110 * ( 5 / 18 ) ] m/sec

= ( 550 / 18 ) m/sec.

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

∴ Distance covered = 500 m.

Time = Distance / Speed

Required time = [ 500 * ( 18 / 550 ) ]

= ( 10 * 18 ) / 11

= 180 / 11

= 16.36 sec

Time taken is 16.36 seconds.

3. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

Answer: 36 km/hr.

Explanation:

Let the speed of each train be x m/sec.

Then, relative speed of the two trains = 2x m/sec.

So, 2x = [ (120 + 120) / 12 ]

2x = 20

x = 10.

∴ Speed of each train = 10 m/sec

= [ 10 * (18/5) ]km/hr

= 2 * 18

= 36 km/hr

Speed of the train is 36 km/hr.

4. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Answer: 12 sec.

Explanation:

Speed of the first train = ( 120/10) m/sec

= 12 m/sec.

Speed of the second train = ( 120 /15 ) m/sec

= 8 m/sec.

Relative speed = (12 + 8)

= 20 m/sec.

∴ Required time = [ (120 + 120) / 20 ] sec

= 240 / 20

= 12 sec.

At 12 seconds they will cross each other.

5. A train takes 12 sec to pass a signal post and covers a distance of 15 km in 15 min. Find the length of train?

Answer: 200 m

Explanation:

Time = 15 min

= ( 15 / 60 )hr

Formula, Speed = Distance / Time

= 15 / ( 15 / 60 )

= ( 15 * 60 ) / 15

= 60 km / hr

= 60 * ( 5 / 18 ) m / sec [ x km/hr = x * ( 5 / 18 ) m/sec ]

= 10 * ( 5 / 3 ) m / sec

= ( 50 / 3 ) m / sec

Formula, Distance = speed * time

Length of the train = ( 50 / 3 ) * 12

= 50 * 4

= 200 m

Length of the train = 200 m

Conclusion

In this article, we see the Train aptitude problems. We hope it enhances your knowledge. The Trains based sums are really interesting and the easiest ones that everyone is able to understand quickly. If you are not preparing for competitive examples, learn this given Train sums with formulas for your higher studies.