PROBLEMS ON TRAINS WITH SOLUTIONS

About "Problems on Trains with Solutions"

Problems on Trains with Solutions :

In this section, we are going to learn, how to solve problems on trains step by step. 

Before look at the problems on trains, you would like to know the shortcuts which are much required to solve problems on trains, 

Please click here

Problems on Trains With Solutions

Problem 1 :

If the speed of a train is 20 m/sec, find the speed the train in kmph. 

Solution :

Speed  =  Distance / Time

Speed  =  20 m/sec

Speed  =  20 x 18/5 m/sec

Speed  =  72 kmph

Hence, the speed of the train is 72 kmph. 

Problem 2 :

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform. 

Solution :

Distances needs to be covered to cross the platform is

=  Sum of the lengths of the train and platform

So, distance traveled to cross the platform is

=  300 + 500

=  800 meters

Time taken to cross the platform is

=  Distance / Speed 

=  800 / 20

=  40 seconds

Hence, time taken by the train to cross the platform is 40 seconds. 

Problem 3 :

A train is running at a speed of 20 m/sec.. If it crosses a pole in 30 seconds, find the length of the train in meters. 

Solution :

The distance covered by the train to cross the pole is

=  Length of the train 

Given : Speed is 20 m/sec and time taken to cross the pole is 30 seconds

We know,  

Distance  =  Speed  Time 

So,

length of the train  =  Speed  Time

Length of the train  =  20  30

Length of the train  =  600 meters

Hence, length of the train is 600 meters.

Problem 4 :

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).

Solution :

Relative speed of the train to man  =  54 - 6  =  48 kmph 

=  48  5/18 m/sec

=  40/3 m/sec 

When the train passes the man, it covers the distance which is equal to its own length in the above relative speed 

Given : It takes 12 seconds for the train to cross the man

So, the length of the train  =  Relative Speed x Time

=  (40/3)  12

=  160 m 

Speed of the train  =  54 kmph

=  54  5/18 m/sec

=  15 m/sec 

When the train crosses the platform, it covers the distance which is equal to the sum of lengths of the train and platform

Given : The train takes 20 seconds to cross the platform. 

So, the sum of lengths of train and platform

=  Speed of the train  Time 

=  15 x 20

=  300 meters

That is, 

Length of train +  Length of platform  =  300

160  +  Length of platform  =  300

Length of platform  =  300 - 160 

Therefore, length of platform  =  140 meters

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

Problem 5 :

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). 

Solution :

When two trains are running in opposite direction,

relative speed  =  60 + 48

=  108 kmph

=  108  5/18 m/sec

=  30 m/sec 

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

Then, sum of the lengths of two trains  is

= Speed  Time

=  30  15  

=  450 m 

When two trains are running in the same direction,

relative speed  =  60 - 48  

= 12 kmph

= 12 ⋅ 5/18  

=  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  =  36  10/3  =  120 m 

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

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

Apart from the problems given above, if you need more problems on trains, please click the following links. 

Problems on Trains with Solutions - 1

Problems on Trains with Solutions - 2

After having gone through the stuff given above, we hope that the students would have understood "Problems on trains with solutions". 

Apart from the stuff given above, if you want to know more about "Problems on trains with solutions", please click here

Apart from the stuff "Problems on trains with solutions", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

HTML Comment Box is loading comments...