UNITARY METHOD
The unitary method is a way of finding the value of a unit of a quantity, given the value of a certain number of that quantity. The value of the unit quantity can be then used to find the value of any number of the quantity.
1) When we know the value of a given quantity, we can use the unitary method to find the value of a unit quantity, and then find the value of the required quantity
If it is a direct variation that is more quantity means more value or less quantity mean less value than to find the value for a unit quantity then we use division and then to find the value for the required quantity we use multiplication.
If it is an indirect variation, that is more quantity means less value or less quantity means more value then to find the value for a unit quantity we use multiplication, and then to find the value for the required quantity we use division.
2) To find the value of a required quantity by the proportion method, we assume that, the value is 'x'.
a) If there is a matter of direct variation then the ratio of the values of one kind of like quantities is equal to the ratio of the other kind of like quantities. This gives an equation in 'x', which we solve to find the required quantity.
b) if it is a case of indirect variation then the ratio of the values of one kind of like quantities is equal to the inverse ratio of the other kind of like quantities
3) when the quantity and value are in direct proportion, multiplying ratio is the final quantity : original quantity, and when they are in inverse proportions then the multiplying ratio is the original quantity : final quantity
Example.1) If the cost of 6 burgers is $ 18, then find out the cost of 20 burgers.
Ans.) As per the given condition, If the cost of 6 burgers $ 18
Then the cost of 1 burger = $ 18 ÷ 6 = $ 3
Then the cost of 20 burger is = $ 3 X 20 = $ 60 (Ans.)
Example.2) If 10 units sugar bag contains 150 kg sugar, but if we add more 75 kg sugar then how more bag to be added? What is the total number of sugar bag required?
Ans.) As per the given condition, 10 no.s bag contains 150 kg sugar
Then, each bag contains = 150 kg ÷ 10 = 15 kg
Now, if each bag contains 15 kg of sugar
Then, to baggage 75 kg sugar requirement of bag is = 75 ÷ 15 = 5 bag
So, we need more 5 sugar bags
Hence we can say that to baggage 150 kg + 75 kg = 225 kg sugar we required 10 + 5 = 15 pcs. Sugar bag (Ans.)
Example.3) If the cost of 20 balls is $ 60, then what is the cost of 100 balls?
Ans.) As per the given condition if the cost of 20 balls is $ 60
Then the cost 1 ball = $ 60 ÷ 20 = $ 3
Now the cost of 100 balls is = $ 3 X 100 = $ 300 (Ans.)