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.

8⋅x  =  18⋅160

x  =  (18⋅160)/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.

7 ⋅ 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.

8 ⋅ 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

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