## DIRECT AND INVERSE VARIATION WORD PROBLEMS WORKSHEET

Question 1 :

If the cost of 8 kg of rice is \$ 160, then the cost of  18 kg rice is

Question 2 :

If the cost of 7 mangoes is 35, then the cost of  15 mangoes is

Question 3 :

A train covers a distance of 195 km in 3 hours. At the same speed, the distance traveled in 5 hours is

Question 4 :

If 8 workers can complete a work in 24 days, then 24 workers can complete the same work in

Question 5 :

If 18 men can do a work in 20 days, then 24 men can do this work in.

Question 6 :

A marriage party of 300 people require 60 kg of vegetables. What is the requirement if 500 people turn up for the marriage ?

Question 7 :

90 teachers are required for a school with a strength 1500 students. How many teachers are required for a school of 2000 students ?

Question 8 :

A car travels 60 km in 45 minutes. At the same rate, how many kilo meters will it travel in one hour? (i)  Solution :

Let x be the required cost

Quantity of rice                  Cost of rice

8                                      160

18                                     x

As the quantity of rice increase, the cost of rice will also increase. It is in direct variation.

8x  =  18160

x  =  (18160)/8

x  = 2880/8

x  =  360

(ii)  Solution :

Let x be the required cost

No of mangoes                  Cost of mangoes

7                                            35

15                                            x

As the number of mangoes increase the cost will also increase. It is in direct variation.

x  =  35  15

x  =  (35  15)/7

x  =  525/7

x  =  75

So, cost of 15 mangoes is \$75.

(iii)  Solution :

Let x be the distance traveled

Distance traveled                Time taken

195                                   3

x                                   5

As time taken by the train increase the distance traveled will also increase. So, it is in direct variation.

195  5  =  x 3

(195  5)/3  =  x

x  =  (195  5)/3

x  =  975/3

x  =  325

So, distance travelled in 5 hours is 325 km.

(iv)  Solution :

Let x be the number of days taken

Number of workers                     Number of days

8                                            24

24                                           x

If number of workers increase, then the number of days will decrease. So, it is under inverse variation.

24  =  24  x

x  =  (8  24)/24

x  =  8 days

So, number of days taken by 24 workers to complete the work is 8 days.

(v)  Solution :

Let x be the number of days taken

Number of workers                    Number of days

18                                    20 days

24                                      x

If number of workers increase, then the number of days will decrease. So, it is under inverse variation.

18. 20  =  24. x

x  =  (18. 20)/24

x  =  360/24

x  =  15 days

So, 24 men can do this work in 15 days.

(vi)  Solution :

Let x be the required quantity of vegetable

Number of people                   Quantity of vegetable

300                                        60

500                                         x

For more number of people, we need more quantity of vegetables. It is in direct variation.

300 . x  =  500 . 60

x  =  (500 .  60)/300

x  =  30000/300

x  =  100 kg

So, the quantity of vegetable needed is 100 kg.

(vii)  Solution :

Let x be the required number of teachers

Number of teachers             Number of students

90                                1500

x                                  2000

To teach more number of students, we need more teachers. So, it is under direct variation.

90 . 2000  = 1500 . x

x  =  (90 . 2000)/1500

x  =  180000/1500

x  =  120 teachers

So, 120 teachers are required to teach 2000 students.

(viii)  Solution :

Let x be the distance taken by car to cover the distance in one hour

Distance covered                 Time taken

60                                        45

x                                       60

We are taking more time, so distance covered by the train will also be more. So, it is in direct variation.

60 . 60  = 45 . x

x  =  (60 . 60)/45

x  =  3600/45

x  =  80 km Apart from the stuff given in this section, 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

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear 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

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 