PROBLEMS ON TRAINS

About the topic "problems on trains"




Problems on trains play a major role quantitative aptitude test. There is no competitive exam without the questions from this topic. We have already learned this topic in our lower classes.Even though we have already been taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

Points to remember

1.To convert km/hr in to m/sec, we need to multiply the given value by 5/18.
2.To convert m/sec in to km/hr, we need to multiply the given value by 18/5.
3.If the length of the train is "l"meters, time taken by the train to pass a standing man or a pole or a signal is equal to the time taken by the train to cover "l" meters.
4.If the length of the train is "l"meters, time taken by the train to pass an object of length "a" meters is time taken by the train to cover (l+a) meters.
5. If two trains are moving on the same directions with speed of "p" m/sec and "q" m/sec (here p > q), then their relative speed is (p-q)m/sec.
6.If two trains are moving opposite to each other in different tracks with speed of "p" m/sec and "q" m/sec, then their relative speed is (p+q)m/sec.
7.Let "a" and "b" are the lengths of the two trains.They are traveling on the same direction with the speed "p" m/sec and "q" m/sec(here p > q),then the time taken by the faster train to cross the slower train = (a+b)/(p-q) seconds.
8. Let "a" and "b" are the lengths of the two trains.They are traveling opposite to each other in different tracks with the speed "p" m/sec and "q" m/sec,then the time taken by the trains to cross each other = (a+b)/(p+q) seconds.
9.Two trains leave at the same time from the stations P and Q and moving towards each other.After crossing, they take "p" hours and "q" hours to reach Q and P respectively.Then the ratio of the speeds of two trains is square root (q) : square root (p)

Why do students have to study this topic?

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic problems on trains. Whether a person is going to write placement exam to get placed or a student is going to write a competitive exam in order to get admission in university, they must be prepared to solve problems on trains. This is the reason for why people must study this topic.

Benefit of studying this topic

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare the problems on trains. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

How can students do time and work problems?

Students have to learn few basic operations in this topic time and work and some additional tricks. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to do the problems which are being asked from this topic in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time. 

Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve problems related to trains. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some problems on trains . You can check your answer online and see step by step solution.

1. It takes 20 seconds for a train running at 54 kmph to cross a platform.And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 kmph in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

             (A) 110, 120                    (B) 160, 120
             (C) 150, 110                    (D) 160, 140

jQuery UI Accordion - Default functionality
Let "x" and "y" be the lengths of the train and platform respectively

Relative speed of the train to man = 54-6 = 48 kmph
= 48X5/18 m/sec = 40/3 m/sec

When train passes the man, it covers its own length in the above relative speed

Length of the train = Relative Speed X Time =(40/3)X12=160 m

And,speed of the train=54 kmph=54X5/18 m/sec = 15 m/sec
The train takes 20 seconds to cross the platform.
That is, the train takes 20 seconds to cover (x+y)m distance

Distance/Speed = Time
(x+y)/15=20--->160+y = 300---> y = 140 m

Hence the lengths of the train and platform are 160 m and 140 m respectively

2. Two trains running at 60 kmph and 48 kmph cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).  

            (A) 330, 120                   (B) 280, 140
            (C) 340, 120                   (D) 290, 140

jQuery UI Accordion - Default functionality
When the two train running in opposite direction, relative speed = 60+48 = 108 kmph = 108X5/18 m/sec = 30 m/sec

Sum of the lengths of the two trains = sum of the distances covered by the two trains in the above relative speed

Sum of the lengths of the two trains = 30X15 = 450 m

When the two trains running in the same direction, relative speed = 60-48 =12 kmph = 12X5/18 = 10/3 m/sec

When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train.

Length of the slower train = 36X10/3 = 120 m

Length of the faster train = 450-120 = 330 m

Hence, the length of the two trains are 330m and 120m

3. Two trains of length  250m and 200m run on parallel lines. When they run in the same direction, it will take 30 second to cross each other. When they run in opposite direction, it will take 10 seconds to cross each other. Find the speeds of the two trains (in kmph).  

            (A) 112, 62                    (B) 110, 58
            (C) 108, 54                    (D) 106, 52

jQuery UI Accordion - Default functionality
Let the speeds of the two trains be S1 and S2

Total distance covered to cross each other = 250 + 200 = 450 m
(when they run in opposite direction or same direction)

When they run in opposite direction, relative speed --> S1 + S2 = 450/10
S1 + S2 = 45 -----(1)
When they run in the same direction, relative speed --> S1 - S2 = 450/30
S1 + S2 = 15 -----(2)

Solving the above two equations, we get

S1 = 30 m/sec = 30X18/5 kmph = 108 kmph
S2 = 15 m/sec = 15X18/5 kmph = 54 kmph

Hence, speeds of the two trains are 108 kmph
and 54 kmph.

4. Find the time taken by a train 100m long running at a speed of 60 kmph to cross another train of length 80 m running at a speed of 48 kmph in the same direction. 

            (A) 54 sec                    (B) 58 sec
            (C) 62 sec                    (D) 66 sec

jQuery UI Accordion - Default functionality
Total distance covered to cross each other = 100 + 80 = 180 m
(when they run in opposite direction or same direction)

Relative speed of the two trains = 60-18 = 12 kmph (running in the same direction)
= 12X5/18 = 10/3 m/sec

Time taken to cross each other = Distance/Speed

= 180/(10/3) seconds
=180X3/10 seconds
=54 seconds

Hence, time taken to cross each other = 54 seconds.

5. Two trains of equal length are running on parallel lines in the same direction at 46 kmph and 36 kmph. The faster train crosses the slower train in 36 seconds. The length of each train is  

            (A) 48 m                          (B) 50 m
            (C) 52 m                          (D) 54 m

jQuery UI Accordion - Default functionality

Let "x" be the length of each train

Total distance covered to cross each other = Sum of the lengths of the two trains

Total distance covered to cross each other = x+x =2x m

Relative speeds of the two trains = 46-36 = 10 kmph
= 10X5/18 = 25/9 m/sec

Distance = Speed X Time
2x = (25/9)X36 m
2x = 100 m
x = 50 m

Hence, the length of each train is 50 m

6. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

            (A) 9 a.m                          (B) 10 a.m
            (C) 11 a.m                       (D) 12 p.m

jQuery UI Accordion - Default functionality
Let the trains meet each other x hours after 7 a.m.

Distance covered by A in x hrs = Speed X Time
= 20x km

Distance covered by B in (x - 1) hrs = 25(x - 1) km (Since B starts 1 hour later (8.00 am), time (B)= x-1)

At the meeting point,
Distance covered A + Distance covered by B = Total distance (from A to B)

20x + 25 (x-1) = 110

Solving the above equation, we get x = 3 hrs.
That is, 3 hrs after 7 a.m is 10 a.m.

Hence, the time at which they will meet is 10 a.m.

7. Two trains are running at 40 kmph and 20 kmph respectively in the same direction .Faster train completely passes a man who is sitting in the slower train in 9 seconds. What is the length of the faster train? 

            (A) 47 m                          (B) 48 m
            (C) 49 m                          (D) 50 m

jQuery UI Accordion - Default functionality
Relative speed of two trains = 40-20 = 20 kmph = 20X5/18 = 50/9 m/sec

Faster train completely passes a man who is sitting in the slower train in 9 seconds.(Given)

The distance covered by the faster train in this 9 seconds = Length of the faster train

The discovered by the faster train in this 9 seconds = Speed X Time
= (50/9)X 9 = 50 m

Hence, the length of the faster train is 50 m.

8. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

             (A) 4:5                    (B) 6:7
             (C) 3:2                    (D) 1:2

jQuery UI Accordion - Default functionality
Let"x" m/sec and "y" m/sec be the speeds of two trains respectively

Then, length of the first train = 27x
Length of the second train = 17y

They cross each other in 23 seconds (Given)

The distance covered by both the trains in this 23 seconds = Sum of the lengths of the two trains
So, the distance covered by the two trains = 27x+17y
Relative speed of the two trains = x+y

Distance/Speed = Time

(27x+17y)/(x+y) = 23
27x + 17y = 23x + 23y
4x = 6y
x/y = 6/4 = 3/2

Hence, the ratio of their speeds is 3:2

9. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

             (A) 240 m                    (B) 250 m
             (C) 260 m                    (D) 270 m

jQuery UI Accordion - Default functionality
Speed of the train = 54 kmph = 54X5/18 m/sec = 15 m/sec

The train passes the man in 20 seconds
Then,length of the train = 20X15 = 300 m

Let "x" be the length of the platform
The train passes the platform in 36 seconds
The distance covered by the train in this 36 seconds = Sum of the lengths of the train and platform
So, the distance covered by the train in this 36 seconds = 300+x

Distance/Speed = Time

(300+x)/15 = 36
300+x = 540
x = 540-300 = 240 m

Hence, the length of the platform is 240 m

10. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the two trains to cross each other is

             (A) 46 sec                    (B) 47 sec
             (C) 48 sec                    (D) 49 sec

jQuery UI Accordion - Default functionality
Relative speed = 60+90 = 150 kmphr = (150X5/18) m/sec = (125/3) m/sec

When they cross each other, distance covered by both the trains = sum of the lengths of the two trains
So,the distance covered by them = 1.1+0.9 = 2 km = 2X1000 m = 2000 m

Time = Distance/Speed

Time = 2000/(125/3) = 2000X3/125 = 48 sec

Hence, time taken by the two trains to cross each other is 48 seconds

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