Basic quantitative aptitude forms an integral part of competitive exam questions. It tests the logical and problem-solving skills of an individual. Mathematics constitutes a major portion of quantitative aptitude questions and has various topics from which problems are asked to solve. These topics include profit and loss, percentage, statistics, time and work, train problems, etc. These are frequently asked questions, and it is necessary to have a firm grip on the basic concepts of speed, distance, and time so that an individual can solve the problems on trains.
The concept of train problems
Some important terms that one should know before attempting problems on a train are:
Length of a train.
Speed of a train.
Distance covered by a train.
Time is taken to cover some distance by train.
The relative speed of trains.
The direction of the moving train.
As train problems are an extension of the topic: of speed, distance, and time, the basic formulas that are used for solving questions on a train are:
Speed = Distance/Time
Distance = Speed * Time
Time = Distance/Speed
There is a lot variety of questions on trains. Basic problems involving the above three formulas are common, but the range of questions can be extended further to more difficult ones involving two trains or one train and one stationary object. Two train questions can be further divided into trains moving in the same direction and trains moving in opposite directions.
If the trains are moving in the same direction, then the relative speed of the two trains will be the difference between the speed of each train. Whereas, if the trains are moving in the opposite direction, then the relative speed of the trains will be the sum of the speed of each train.
In the case of distance, the direction of the trains will not matter. For both cases, the total distance covered will be equal to the sum of the lengths of each train.
For trains moving past a stationary object, the distance traveled will be equal to the length of the train, while for moving past platforms and bridges, the total distance traveled will be equal to the sum of the length of the train and the length of the bridge/platform.
Important formulas for moving trains
If there are two trains ‘A’ and ‘B’ and the lengths of the train are ‘x’ and ‘y’ and the speed of the train ‘a’ and ‘b’, respectively, then for trains moving in the same direction,
Time is taken by both the trains to cross each other = (a+b)/(x-y)
and relative speed = x-y.
For trains moving in the opposite direction,
time taken by both trains to cross each other = (a+b)/(x+y)
and relative speed = x+y.
If the train of length ‘x’ with speed ‘a is moving past a stationary object, then the time is taken by the train to cross the object = x/a.
If the train of length ‘x’ with speed ‘a’ is moving past the bridge/platform of length ‘y’, then the time is taken by the train to cross the bridge/platform = ((x+y)/a)
Tips and Tricks on train problems
Tip 1: Carefully understand the context of the question.
Tip 2: Determine the directions of the moving trains and list down the details already provided about the trains.
Tip 3: Keep the units the same for all values.
Example
A train is moving at a speed of 90 km/hr and crosses another train moving in the same direction at 180 km/hr in 30 seconds. What is the sum of the lengths of the two trains?
Answer:
Speed of train B = 180 km/hr = (180*(5/18))= 50 m/sec.
Trains are moving in the same direction.
Hence,
Relative speed = (50-25) m/sec = 25 m/sec
Time taken by train A to cross train B = 30 secs
Sum of the length of the trains = distance travelled
Distance = Speed * Time = (25*30) = 750m
Hence the Sum of the length of the train = 750m.
Conclusion
The train problems aptitudes are compulsory for all kinds of competitive exams. It is also important and given in every school math test. Finding the train, its time, and speed are relevant to our daily lives and have always been the most common math problem. To master the problems on train formulas and some important tricks should be always remembered.
