Learn Class 8 Math - Direct and Inverse Variations

Inverse Proportions

If the cost of variable decreases or increases upon corresponding growth or lower within the cost of variable, then we will say that variables are in inverse proportion.

In simple words, variables or portions are proportional to every difference. If one is varied, then the alternative also adjusts using a hard and fast amount.

This belonging of variables is named proportionality, and the image used to symbolize the proportionality is "∝."

There are forms of proportionality of variables. They are:

  • Directly Proportional
  • Inversely Proportional

Relation for Inverse Proportion

Considering variables and establishes the relation for inverse proportionality among and, in which is a constant.

Direct Proportion

Direct share is a mathematical assessment among numbers in which the ratio of the 2 numbers is identical to a steady value. The share definition says that once ratios are equivalent, they're in share.

The symbol used to narrate the proportions is "∝".

Relation for Direct Proportion

Considering variables x and y, frac = k or x=ky establishes the easy relation for direct share among x and y, in which ok is a constant.

Direct and Inverse Variations Sample Questions for Class 8

Question 1

If 30 metres of cloth costs ₹2250, how many metres of cloth can be bought in ₹5650?
A. 75.33 m
B. 78 m
C. 79.45m
D. 76.13 m

Question 2

There is rice bags which can last for 70 days for 45 people. If 7 more people join, how many days will the rice bags last?
A. 56 days
B. 68 days
C. 61 days
D. 59 days

Question 3

A person has money to buy 60 books worth ₹ 350 each. How many books can he buy if cost of each book is decreased by ₹50?
A. 80
B. 70
C. 75
D. 65

Question 4

x is directly proportional to y. x = 42 and y = 210. What is the value of constant of proportionality?
A. 1/5
B. 5
C. 8820
D. 1/8820

Question 5

x is inversely proportional to y. x = 72 and constant of proportionality is 12. What is value of y?
A. 6
B. 1/6
C. 864
D. None of the above