# DIRECT VARIATION AND INVERSE VARIATION WORKSHEET

## About "Direct Variation and Inverse Variation Worksheet"

Direct Variation and Inverse Variation Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on direct variation and inverse variation.

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## Direct Variation and Inverse Variation Worksheet - Problems

Problem 1 :

75 basketballs cost \$1143.75. Find the cost of 26 basketballs.

Problem 2 :

7 men can complete a work in 52 days. In how many days will 13 men finish the same work ?

Problem 3 :

If David sells 2 gallons of juice for \$4, how much money will he get by selling 17 gallons of juice ?

Problem 4 :

A book contains 120 pages and each page has 35 lines. How many pages will the book contain if every page has 24 lines per page ?

Problem 5 :

The cost of a taxi is \$40.50 for 15 miles. Find the cost for 20 miles.

Problem 6 :

A truck covers a particular distance in 3 hours with the speed of 60 miles per hour. If the speed is increased by 30 miles per hour, find the time taken by the truck to cover the same distance.

Problem 7 :

In a business, if A can earn \$7500 in 2.5 years, At the same rate, find his earning for 4 years.

Problem 8 :

David can complete a work in 6 days working 8 hours per day. If he works 3 hours per day, how many days will he take to complete the work ?

Problem 9 :

In 36.5 weeks, Miguel raised \$2,372.50 for cancer research. How much money will he raise 20 weeks ?

Problem 10 :

Alex  takes 15 days to reduce 30 kilograms of his weight by doing 30 minutes exercise per day. If he does exercise for 1 hour 30 minutes per day, how many days will he take to reduce the same weight ?

Problem 11 :

Shanel gets 2/ 5 of a dollar for 1/7 hour of work. How much money does she get for 3 hours ?

Problem 12 :

If 5 men can paint a house in 18 hours, how many men will be able to paint it in 10 hours ?

Problem 13 :

In a fort, 360 men have provisions for 21 days. If 60 more men join them, how long will the provision last ?

Problem 14 :

John ordered 330 units of a product for \$495. Then he reduced his order to 270 units. How much money does John have to pay for 270 units ?

Problem 15 :

A man can type 9 pages of a book everyday and completes it in 50 days. How many days will he take to complete it, if he types 15 pages everyday ?

## Direct Variation and Inverse Variation Worksheet - Solutions

Problem 1 :

75 basketballs cost \$1143.75. Find the cost of 26 basketballs.

Solution :

This is a situation of direct variation.

Because,

less number of basket balls -----> cost will be less

Let "m" be the cost of 26 basket balls.

 No. of Basket Balls 7526 Cost1143.75m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

75  m  =  26  1143.75

m  =  (26  1143.75) / 75

m  =  396.50

Hence, the cost of 26 basket balls is \$ 396.50

Problem 2 :

7 men can complete a work in 52 days. In how many days will 13 men finish the same work ?

Solution :

This is a situation of inverse variation.

Because,

more men -----> less days

Let "m" be the required no. of days.

 No. of Men 713 No. of Days52m

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

52  =  13  m

(7  52) / 13  =  m

28  =  m

Hence, 13 men can complete the work in 28 days.

Problem 3 :

If David sells 2 gallons of juice for \$4, how much money will he get by selling 17 gallons of juice ?

Solution :

This is a situation of direct variation.

Because,

more gallons of juice -----> amount received will be more

Let "m" be the required amount of money.

 No. of Gallons 217 Value (in dollars) 4m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

m  =    17  4

m  =  (17  4) / 2

m  =  34

Hence, David will earn \$34 by selling 17 gallons of juice.

Problem 4 :

A book contains 120 pages and each page has 35 lines. How many pages will the book contain if every page has 24 lines per page ?

Solution :

This is a situation of inverse variation.

Because,

less lines -----> more pages

Let "m" be the required number of pages.

 No. of Pages 120m No. of Lines3524

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

120  35  =  m  24

(120  35) / 24  =  m

175  =  m

Hence, if every page has 24 lines per page, the book will contain 175 pages.

Problem 5 :

The cost of a taxi is \$40.50 for 15 miles. Find the cost for 20 miles.

Solution :

This is a situation of direct variation.

Because,

more miles -----> more cost

Let "m" be the required cost.

 No. of Miles 1520 Cost40.50m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

15  m  =  20  40.50

m  =  (20  40.50) / 15

m  =  54

Hence, the cost for 20 miles is \$54.

Problem 6 :

A truck covers a particular distance in 3 hours with the speed of 60 miles per hour. If the speed is increased by 30 miles per hour, find the time taken by the truck to cover the same distance.

Solution :

This is a situation of inverse variation.

Because,

more speed -----> less time

If the given speed 60 mph is increased by 30 mph,

then the new speed  =  90 mph

Let "m" be the required time

 No. of hours 3m Speed6090

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

60  =  m  90

(3  60) / 90  =  m

2  =  m

Hence, if the speed is increased by 30 mph, time taken by the truck is 2 hours.

Problem 7 :

In a business, if A can earn \$7500 in 2.5 years, At the same rate, find his earning for 4 years.

Solution :

This is a situation of direct variation.

Because,

more time  -----> more earning

 No. of Years 2.54 Earning7500m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

2.5 ⋅ m  =  4  7500

m  =  (4  7500) / 2.5

m  =  12000

Hence, the earning for 4 years is \$12000.

Problem 8 :

David can complete a work in 6 days working 8 hours per day. If he works 3 hours per day, how many days will he take to complete the work ?

Solution :

This is a situation of inverse variation.

Because,

less hours per day-----> more days to complete the work

Let "m" be the required number of days.

 No. of Days6m No. of Hours 83

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

8  =  m x 3

(6  8) / 3  =  m

16  =  m

Hence, David can complete the work in 16 days working 3 hours per day.

Problem 9 :

In 36.5 weeks, Miguel raised \$2,372.50 for cancer research. How much money will he raise 20 weeks ?

Solution :

This is a situation of direct variation.

Because,

less number of weeks ----> amount raised will be less

Let "m" be the required amount of money.

 Weeks36.520 Amount of Money2372.50m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

36.5  m  =  20  2372.50

m  =  (20  2372.50) / 36.5

m  =  1300

Hence, the money raised in 20 weeks is \$1300.

Problem 10 :

Alex  takes 15 days to reduce 30 kilograms of his weight by doing 30 minutes exercise per day. If he does exercise for 1 hour 30 minutes per day, how many days will he take to reduce the same weight ?

Solution :

This is a situation of inverse variation.

Because,

more minutes per day----> less days to reduce the weight

And also

1 hour 30 minutes per day  =  90 minutes per day

Let "m" be the required number of days.

 No. of Days15m No. of Minutes3090

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

15  30  =  m  90

(15  30) / 90  =  m

5  =  m

Hence, if Alex does exercise for 1 hour 30 minutes per day, it will take 5 days to reduce 30 kilograms of weight.

Problem 11 :

Shanel gets 2/ 5 of a dollar for 1/7 hour of work. How much money does she get for 3 hours ?

Solution :

This is a situation of direct variation.

Because,

more hours -----> more earning

 No. of Hours1/73 Dollars2/5m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

1/7  m  =  3  2/5

m  =  7  6/5

m  =   42 / 5

m  =  8.4

Hence, Shanel gets \$8.4 for 3 hours of work.

Problem 12 :

If 5 men can paint a house in 18 hours, how many men will be able to paint it in 10 hours ?

Solution :

This is a situation of inverse variation.

Because,

less hours  -----> more men

Let "m" be the required number of men.

 No. of Men5m No. of Hours1810

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

18  =  m  10

90 / 10  =  m

9  =  m

Hence, 9 men will be able to paint the house in 10 hours.

Problem 13 :

In a fort, 360 men have provisions for 21 days. If 60 more men join them, how long will the provision last ?

Solution :

This is a situation of inversion  variation.

Because,

more men -----> provision will last for less days

Given : 360 men -----> 21 days

If 60 more men join, then

the total number of men  =  420

Let "m" be the required number of days.

 No. of Men360420 No. of Days21m

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

360  21  =  420  m

(360  21) / 420  =  m

18  =  m

Hence, if 60 more men join, provision will last for 18 days.

Problem 14 :

John ordered 330 units of a product for \$495. Then he reduced his order to 270 units. How much money does John have to pay for 270 units ?

Solution :

This is a situation of direct variation.

Because,

less units -----> less cost

Let "m" be the required amount of money

 No. of Units330270 Money495m

Since this is direct variation, we have to apply the shortcut "cross multiplication"

330  m  =  270  495

m  =  (270  495) / 330

m  =  405

Hence, John has to pay \$405 for 270 units.

Problem 15 :

A man can type 9 pages of a book everyday and completes it in 50 days. How many days will he take to complete it, if he types 15 pages everyday ?

Solution :

This is a situation of inverse variation.

Because,

more pages per day-----> less days to complete the book

Let "m" be the required number of days

 No. of Days50m No. of Pages915

Since this is inverse variation, we have to apply the shortcut "straight multiplication"

50  9  =  m  15

450 / 15  =  m

30  =  m

Hence, the man will complete the book in 30 days, if he types 15 pages per day.

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