Page 103 - ICSE Math 8

EXERCISE 9.2

1. Which of the following are in inverse variation with each other?
(a) The number of burgers (n) you can buy with ` 150 and the cost (c) of each burger
(b) The time taken to finish a given work and the number of men doing that work
(c) The amount of petrol used and the distance travelled by a car
(d) The number of children in a birthday party and the amount of food consumed
(e) Time taken to cover a given distance with variation in speed of a vehicle
2. In which of the given tables, x and y are in inverse variation with each other?

(a) x 2 4 3 8 12 (b) x 6 4 12 30 15

y 16 8 12 4 3 y 10 15 5 2 4

3. Fill in the missing entries if x and y vary inversely:

(a) x 45 ... 10 ... 30 (b) x ... 12 16 ... 15
y 2 15 ... 18 ... y 10 20 ... 30 ...

4. A hostel mess has provisions for 200 students for 30 days. If 100 new students join the hostel, how long
will the provisions last?
5. If Kinjal reads 8 pages daily, she can finish a book in 15 days. How many pages does Kinjal read daily
if she finishes the book in 10 days?
6. Five spraying machines working together can finish painting a house in 36 minutes. If 2 machines break
down, then in how much time can the remaining machines complete the job?
7. Rahul and Chunky start together from Delhi in their own cars for Shimla. Rahul drives at an average
speed of 60 km/h and reaches Shimla in 9 hours. If Chunky drives at an average speed of 54 km/h, how
much time will he take to reach Shimla?
8. Reena has enough money to buy 10 kg of potatoes worth ` 18/kg with the same money. How many
kilograms of potatoes can she buy if the price of potatoes increases to ` 20/kg?
9. A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using
20 bottles in each box, how many boxes would be filled?
10. If x is in inverse variation with y and
(a) x = 4, y = 6, find x, when y = 12.
(b) x = 7, y = 4, find y, when x = 2.
(c) x = 20, find y when constant of variation is 300.
(d) y = 16, find x when constant of variation is 176.

Applications of Direct and Inverse Variations

In this section, we will learn some application of direct and inverse variations in real life situations such as
solving problems involving time and work and pipes and cisterns.

Time and Work
Time is directly proportional to work. In other words, more the amount of work done by a person, more is the
time needed to do it.
 1

If a person completes a work in n days, then the work completed by the person in one day is   . Conversely,

n
 1
if a person completes   work in one day, then the person will take n days to complete the work.

n
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