Types of Proportion:
There are four types of proportion.

Direct Proportion

Inverse Proportion

Compound Proportion

Continued Proportion
Direct Proportion:
Suppose the price of one piece of soap is 20 Rs.
If a person wants to buy one dozen pieces of soap, then he has to pay 240 Rs. If he wants to buy two dozen pieces of soap, he has to pay 480 Rs and so on.
We can easily see that if the person buys more pieces, he has to pay more or he has to pay less if he buys less pieces.
That is, as pieces of soap are increased total price also increased, conversely, if pieces of soap are decreased total price also decreased. In such situation, we say that pieces and price are directly related.
In other words, If increase in one quantity causes increase in other quantity or decrease in one quantity causes decrease in other quantity, then we say that they are related directly (They are direct proportion).
If and are in direct proportion, then division of and will be constant.
i.e.
In the above example, we see that
each ratio is the same.
Hence, if we are dealing with quantities, which are related directly, (which are in direct proportion), then we shall use the follow rule.
24 x 240 = 12 x 480
In general
Principle of Direct Proportion
Example:
If 30 dozens of eggs cost 300 Rs. Find the cost of 5dozens of eggs.
Solution:
Let be the required price of 5 dozens eggs
Since quantities are in direct proportion, so we use the above principle.
x 30 = 5 x 300
= 50 Rs.
Example:
A car travel 81 km in 4.5 liters. How far will it goes by 20 liters of petrol.
Solution:
Let be required required distance travelled by car in 20 liters.
Since quantities are related directly, so by the above principle
4.5 x = 20 x 81
= 360 km
