QUADRATIC WORD PROBLEMS WORKSHEET WITH ANSWERS

Problem 1 :

The speed of a boat in still water is 15 km/hr. It goes 3 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.

Solution :

Let x km/hr be the speed of water

Speed of boat is 15 km/hr

So speed is upstream  =  (15+x) km/hr

Speed in downstream  =  (15–x) km/hr

Let T1 be the time taken to cover the distance 30 km in upstream

Let T2 be the time taken to cover the distance 30 km in downstream

Time  =  Distance/Speed

T1  =  30/(15 + x)

T2 =  30/(15 - x)

T1 + T2  =  4 hours 30 minutes

T1 + T2  =  4  1/2

[30/(15 + x) + 30/(15 - x)]  =  9/2

30[1/(15 + x) + 1/(15 - x)]  =  9/2

30 [(15 – x + 15 + x)/(225 - x²)]  =  9/2

30 (30)/(225 - x2)  =  9/2

900 ⋅ 2  =  9 (225 - x²)

By dividing the equation by 9, we get

200  =  (225 - x2)

225 - x2  =  200

225 – 200  =  x2

x =  25

x  =  √25

x  =  ± 5

Speed must be positive. 

So,

speed of water  =  5 km/hr.

Problem 2 :

One year ago a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present age.

Solution :

Let x be the present age of son and y be the age of father.

So (x-1) be the age of son one year ago.

(y-1) be the age of father one year ago.

By using the given information

y  =  x2 -----(1)

y – 1  =  8(x -1)

y  =  8x – 7 -----(2)

(1)  =  (2)

x² =  8x – 7

x²- 8x + 7  =  0

(x -1)(x – 7)  =  0

x-1  =  0

x  =  1

x-7  =  0

x  =  7

So, present age of son is 7 years.

Problem 3 :

A chess board contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of chess board. 

Solution :

Let x be the side length of the square board

Area of one square in the chess board  =  6.25 cm2

Area of 64 squares  =  64 (62.5)

(x – 4)2  =  400

(x – 4)   =  400

x-4  =  20

x = 24 cm

Therefore side length of square shaped chess board is 24 cm.

Problem 4 :

A takes less than the time taken by B to finish the piece of work. If both A and B together can finish the work in 4 days. Find the time that B would take to finish the work by himself.

Solution :

Let x be the tune taken by B to finish the work.

So (x – 6) be the time taken by to finish the work.

Work done by A in one day  =  1/x

Work done by B in one day  =  1/(x - 6)

Number of days taken by both to finish the work  =  1/4

1/x + 1/(x-6)  =  1/4

(2x - 6)/(x2 – 6x)  =  1/4

4(2x - 6)  =  x2 – 6x

8x – 24  =  x– 6x

x2 – 14x + 24  =  0

(x – 2) (x – 12)  =  0

x-2  =  0

x  =  2

x-12  =  0

x  =  12

So, B is taking 12 days to complete the work.

Problem 5 :

Two trains leave railway stations at the same time. The first train travels due west and the second train due north. The first travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, find the average speed of each train.

Solution :

Let x km/hr be the speed of second train.

So sped of first train will be (x + 5) km/hr

Distance covered by the first train in 2 hours  =  2(x + 5)

Distance covered by the second train in 2 hours = 2x

By using Pythagoras theorem,

 [2(x+5)]2 + (2x)2  =  502

[2x+10]² + (2x)2  =  502

[4x+ 100 + 2(2x)(10)] + 4x2  =  2500

8x2 + 40x + 100 – 2500 = 0

8x2 + 40x – 2400 = 0

By dividing the equation by 8, we get

x2 + 5x – 300  =  0

(x + 20) (x -15)  =  0

x+20  =  0

x  =  -20

x-15  =  0

x  =  15

Therefore speed of the second train is 15 km/hr.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

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

COORDINATE GEOMETRY

Coordinate 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

Coordinate 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