Page 291 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\16_Chapter_12\Chapter_12
\ 06-Jan-2025 Surendra Prajapati Proof-7 Reader’s Sign _______________________ Date __________

4. The variable x varies inversely as y and x is 80 when y is 160. What is y when x is 64?

5. In a camp, there is enough flour for 300 persons for 42 days. How long will the flour last if 50 more
persons join the camp?
6. A train moving at a uniform speed of 72 km/h reaches its destination in 20 hours.

(a) How long will it take if it runs at the speed of 90 km/h?
(b) At what speed will it reach the destination in 24 hours?
7. A contractor undertook a contract to complete a part of a stadium in 9 months with a team of 560
workers. Later on, it was required to complete the job in 5 months. How many extra workers should
he employ to complete the work?
8. The price of sugar is `30 per kg. Akhil can buy 12 kg sugar with the amount of money he has. If the
price of sugar is increased by `10 per kg, how much sugar can Akhil buy?

9. 8 pipes can fill a tank in 1 hour 45 minutes. How long will it take to fill the tank if 10 pipes of the
same type are used?

10. If x varies inversely as the cube of y, when y = 5 and the value of x = 81. What will be the value of y
when x = 3?

11. If y varies inversely as the square root of x, when x = 25 and y = 6. What will be the value of x when y = 5?
12. A factory requires 40 machines to produce a given number of items in 60 days. How many machines
would be required to produce the same number of items in 50 days?

13. 45 horses can graze a field in 8 days. How many less/more horses will graze the same field in
20 days?

14. Rajat distributed a packet of sweets among 35 children in his class and each of them received
6 sweets. If 5 children were absent, how many extra sweets would each child get?

Applications of Variations

There are many real life situations where the concept of direct and indirect variations is used.
In this section, we shall learn how to solve the problems related to ‘Time and Work’, ‘Pipes and
Cistern’, and ‘Time and Distance’ by using these concepts.
Time and Work

We know that,

1. The number of men (M) employed and the amount of work (W) done vary directly, i.e., M ∝ W.
2. For completing a certain work, the number of men (M) and the number of days (d) vary
1
inversely, i.e., M ∝ .
d
3. The amount of work (W) done and the number of days (d) required to do that work vary directly,
i.e., W ∝ d.

While solving problems related to time and work, we use the unitary method. For, this we usually
consider the work done to be equal to 1 and follow the rules as given below:

Rule 1. If a person can do a piece of work in n days or hours, then work done by the person in 1
day or 1 hour is =  1 part of the work.
 

n
Rule 2. Conversely, if a person does 1 part of the work in 1 day, then he will complete the work
in n days. n

289 Direct and Indirect Variations