New Learning Composite Mathematics Class 8 SK Gupta Anubhuti Gangal Variation Chapter 9B Solution

New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 8 Variation Self Practice 9B Solution

(1) State the relationship between the given variables as an equation, using k for the constant of variation.

(a) The volume V a gas at a fixed temperature varies inversely as the pressure P.

(b) The current l in an electrical circuit of fixed voltage varies inversely as the resistance R.

(c) The height h of a cylinder of fixed volume varies inversely as the area A of the base.

(d) The frequency f of an electromagnetic wave is inversely proportional to the length l of the wave.

(2) Fill in the blanks in the following tables by determining first whether x and y very directly or inversely:

(a)

x 3 6 ? 27 ?
y 11 22 33 ? 880

(b)

x 30 20 15 ? ?
y 6 4 ? 2 1

(c)

x 2 3 4 ? 8
y 48 ? 24 16 ?

(d)

x 1 5 10 ? ?
y 125 ? 12.5 5 1

Solution:

(3) (a) If y varies inversely as x, and y = 9 when x = 2. find y when x = 3.

(b) If u is inversely proportional to v, and is u = 12 when v = 3, find u when v = 9.

(c) If c is inversely proportional to d, and if c = 18 when d = 2/3, find d when c = 6/7

(d) If m is inversely propotional to n, and if m = 0.02 when n = 5, find m when n = 0.2

(4) Navin cycles to his school at an average speed of 12 km/hr. It takes him 20 minutes to reach the school. If he wants to reach his school in 15 minutes, what should be his average speed?

(5) The time needed to travel from one place to another is inversely proportional to the speed. A person travelling 72 km/hr can go from Dehradun to Lucknow in 10 hours. How fast must the person travel to make the trip in 9 hours?

Solution: 

(6) 28 pumps can empty a reservoir in 18 hours. In how many hours can 42 such pumps do the same work?

(7) A stock of food grains is enough for 400 persons in 9 days. How long will the same stock last for 300 persons?

(8) A contractor, who had a workforce of 630 persons, undertook to complete a portion of a stadium in 14 months. He was asked to complete the job in 9 months. How many extra persons had he to employ?

(9) Working 4 hours a day, Savita can type a manuscript in 15 days. How many hours a day should she work so as to finish the work in 10 days?

(10) A train moving at a speed of 60 km/hr covers a certain distance in 7.5 hours. What should be the speed of the train to cover the same distance in 6 hours?

Solution:

(11) A garrison of 800 men had provisions for 39 days, However a reinforcement of 500 men arrived. For how many days will the food last now?

(12) A beseieged town has provisions to last for 3 weeks. Its population is 22400. How many people must be sent away in order that the provisions may last for 7 weeks?

(13) A hostel had rations for 60 days for 500 students. After 12 days, 300 more students joined the hostel. How long will the remaining rations last?

Solution:

1 Comment

Add a Comment

Leave a Reply

Your email address will not be published. Required fields are marked *