**Unitary Method**

**Unitary method** is a
popular method in mathematical calculation. This method helps to find the value
of unit quantity from the gross value, and from the value of unit quantity, we
can find the value of required quantity.

In the calculation of unit value, we have
two types of variations. They are direct variation and indirect variation.

**Direct variation **

If two quantities are so related that the
increase or decrease in one causes the corresponding increase or decrease in
the other, they are said to be in **direct
variation**. Let us take an example of no. of copies and their cost:

Above table shows that if the number of
copies increases the total cost also increases. So the number of copies and
their cost are in direct variation. To find the unit value for such quantities
we have to divide the gross value by the number of quantities. And then, we
have to multiply the unit value with the required number of quantities to find
the required value. For example:

“If cost of 5 copies is Rs. 250, find the
cost of 8 copies.”

*Solution: Here,*

*∴** The cost of 8 copies is Rs. 400. *

**Indirect variation**

If two quantities are so related that the
decrease or increase in one causes the corresponding increase or decrease in
the other is called **indirect variation**.
Let us take an example of number of men and their working days:

Above table shows that if the number of
men increases the working days decreases. So the number of men and working days
are in indirect variation. To find the unit value for such quantities we have
to multiply the gross value by the number of quantities. And then, we have to
divide the unit value by the required number of quantities to find the required
value. For example:

“If 4 men can do a work in 5 days, in how
many days 10 men can do the same work?”

*Solution: Here,*

*∴** 10 men can do the same work in 2 days. *

*Worked
Out Examples*

*Worked Out Examples*

*Example 1: If 10 kg of mangoes cost Rs.
500 then what will be the cost for 15 kg?*

*Solution:** Here,*

*∴** 15 kg
mangoes cost Rs. 750.*

*Example 2: The price of 20 books is Rs.
3000. How many books can be bought for Rs. 1950?*

*Solution:** Here,*

*∴** 13 books can be
bought for Rs. 1950.*

*Example 3: If ¾** of a man’s income is Rs. 3000, what will
be ¼ of his income?*

*Solution:** Here,*

*∴** ¼ of his income is
Rs. 1000.*

*Example 4: If a work can be completed by
20 people in 45 days. How long will it take to complete the same work by 15
people?*

*Solution:** Here,*

*∴** It will take 60
days to complete the same work by 15 people.*

*Example 5: A garrison of 800 men has
provision for 120 days. How many men should be added to finish the provision in
100 days?*

*Solution:** Here,*

*Provision is available,*

*∴** 960 – 800 = 160 men
should be added to finish the provision in 100 days.*

*You can comment your
questions or problems regarding the unitary method here.*

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