LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

UNITARY METHOD

__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.)**