Direct and Inverse Proportion Class 8 Notes - Chapter 13

Direct Proportion

There are many situations when we come across two things which are related to each other. When two objects are related, such that an increase or decrease in the value of one object changes the value of the other object, they are said to be in proportion. ∝ is the symbol that is used to denote proportionality.

For two quantities to maintain a direct proportion relationship, they have to be related such that if we double one quantity, the other one also gets doubled. Similarly, if we triple one, the other quantity becomes triple.

Direct proportion is a situation where an increase in one quantity causes a corresponding increase in the other, or a decrease in one quantity causes a corresponding decrease in the other one.

Let us look at some examples to understand more.

In the table below, we can see that if the number of people dresses bought increases, the amount paid will also increase proportionally.



Please note that the unit of quantities remains the same while talking about direct proportion.
Here is one example of how the values decrease together.

If we buy fewer apples, the price to be paid will decrease proportionally.


We have a formula to solve problems based on direct proportion. Let’s read ahead.

Formula

Mathematically, we can say that two quantities x and y are in direct proportion if-

x/y = k, or x = ky

k is called the constant of proportionality.

It is the number that relates the two variables together. While solving problems related to direct proportion, the value of k never changes in the problem, that is, it remains constant.

If x1 and x2 are the two different values of x, whereas, y1 and y2 are the corresponding values of y, then,

X1/Y1 = X2/Y2

Let us see an example.

The cost of 500 grams of sweets is ₹250. How much sweets of the same type can be purchased for ₹420?

Let x grams of sweets be purchased for ₹420.



So, 840 grams of sweet can be purchased for ₹420.

You may also need this
NCERT Solutions for class 8 Maths Chapter 13
NCERT Solutions for class 8 Maths Chapter 13 Exercise 13.1
NCERT Solutions for class 8 Maths Chapter 13 Exercise 13.2

Now, let us read inverse proportion.

Inverse Proportion

When one quantity changes, the other quantity changes in the opposite manner. Such relationship is called an inverse proportion. If the value of one quantity increases, the other will decrease or vice-versa.

For example, if we have more students to eat in a hostel with fixed amount of food, the food will last for fewer number of days. So, it is also an example of inverse proportion.

For two quantities to maintain an inverse proportion relationship, they have to be related such that if we double one quantity, the other gets halved. Similarly, if we triple one, the other quantity becomes one-third. The same is the case for reduction; if we reduce one by half, the other gets doubled.

We have a formula to solve problems based on inverse proportion. Let’s read ahead.

Formula

Mathematically, we can say that two quantities x and y are in inverse proportion if-

xy = k, or x = k/y

If x1 and x2 are the two different values of x, whereas y1 and y2 are the corresponding values of y, then,

x1y1 = x2y2

Note

When two quantities x and y are in inverse proportion, they can be written as-

x ∞ 1/y

Let us see some examples.

Want to study more? Download the free PDFs of class 8 maths

Get PDF of class 8 maths solutions
Maths Worksheets for Class 8
Class 8 Maths Notes
Class 8 Maths NCERT Solutions
Class 8 Maths Syllabus

1. 20 men can finish a piece of work in 34 days. How many days will be taken by 68 men to finish it?

More number of men will take less time to complete the work. So, this is a case of inverse proportion.

Let x be the number of days taken by 68 men to finish the piece of work.

Number of days 34 and x
Number of men 20 and 68

20 × 34 = 68 × x [x1y1 = x2y2]
x = 20 × 34 / 68
x = 40

So, 68 men will take 40 days to finish the piece of work.

2. 1000 men can finish a stock of food in 42 days. How many more men should join them so that the same stock may last for 30 days?

Number of men 1000 x
Days 42 30

Let x be the total number of men after additional men have joined to finish the stock in 30 days.

1000 × 42 = 30 × x [x1y1 = x2y2]
x = 1000 × 42 / 30
x = 1400

Number of additional men required = 1400 – 1000 = 400
So, 400 more men will be required to finish the stock of food in 30 days.

Links to Other Resources for Class 8 Maths

Other Class 8 Maths Related Links
Find surface area of cylinder
Find factors of 32
Finding square root of a decimal number
Calculating area of semicircle
Learn about 2d shapes in math