Direct Variation
Two quantity ‘A’ & ‘B’ are said to vary directly or be in direct variation or in direct proportion if the change in such a way that the ratio of two values of ‘A’ is the same as the ratio of the corresponding two values of ‘B’. Here the cost of any product directly varies with the cost of the particular product.
Example.1) If the cost of 15 roses is $ 30 then find the cost of 20 roses ?
Ans.) If there are the cost of 15 roses is $ 30
Then the cost of 1 rose is = $ 30 ÷ 15 = $ 2
Now the cost of 20 roses is = $ 2 X 20 = $ 40
Here you can observe that, cost & product directly varies, if quantity increase then value increase. (Ans.)
Example.2) If the cost of 15 balls is $ 75, then find the value of 25 balls via unitary, proportion, and multiplying ratio method.
Ans.) Unitary Method
If there are the cost of 15 balls is $ 75
Then the cost of 1 ball is = $ 75 ÷ 15 = $ 5
Now the cost of 25 balls is = $ 5 X 25 = $ 125
Here you can observe that, cost & product directly varies, if quantity increase then value increase.
Proportion Method
Clearly, the greater the number of balls the greater is the value, so the value is directly proportional to the number of balls, suppose x is a value of 25 balls, then the ratio of the numbers = the ratio of the values –
That is 15 : 25 = 75 : x
15 75
------------ = ----------
25 x
15 x = 75 X 25
75 X 25
x = --------------- = 5 X 25 = 125 (Ans.)
15
Multiplying Ratio Method
Here the two quantities (value & number) are in the direct proportion. The number increases in the ratio 15 : 25 = 3 : 5
So, the value also increases in the same ratio, hence the multiplying ratio is 5 : 3
5
So, the required value would be = ----------- X 75
3
= 5 X 25 = 125 (Ans.)