Unitary Method
What is Unitary Method?
Unitary method is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Karan goes to a stationery shop to buy some notebooks.
The shopkeeper informs him that \(2\) notebooks would cost \(\text{Rs.}\;90\)
In this example, the number of books corresponds to the “unit” and the cost of the books corresponds to the “value”.
Can you find the cost of \(5\) notebooks?
Let us first understand unitary method and then revisit this problem.
Different Types of Unitary Method
There are two types of unitary methods because they result in two types of variations.
Direct Variation
This type describes the direct relationship between two quantities.
In simple words, if one quantity increases, the other quantity also increases and viceversa.
For example:
If the speed of a car is increased, it covers more distance in a fixed amount of time.
Indirect Variation
This type describes the indirect relationship between two quantities.
In simple words, if one quantity increases, the other quantity decreases and viceversa.
For example:
Increasing the speed of the car will result in covering a fixed distance in lesser time.
Example of Unitary Method
Ria went to an icecream parlour and bought \(5\) icecreams.
She paid \(\text{Rs.}\;125\) to the shopkeeper.
What would be the cost of \(3\) icecreams?
This may seem hard to calculate! However, we can solve this problem using the unitary method.
First, let us make a note of the information we have.
There are \(5\) icecreams.
\(5\) icecreams cost \(\text{Rs.}\;125\).
STEP 1:
Let’s find the cost of \(1\) icecream.
In order to do that, divide the total cost of icecreams by the total number of icecreams.
The cost of 1 icecream:
\[\begin{align}&=\frac{\text{Total cost of icecreams}}{\text{Total number of icecreams}}\\&=\frac{125}{5}\\&=25\end{align}\]
Therefore, the cost of \(1\) icecream is \(\text{Rs.}\;25\).
STEP 2:
To find the cost of \(3\) icecreams, multiply the cost of \(1\) icecream with the number of icecreams.
Cost of 3 icecreams:
\[\begin{align} &\!= \!\text{Cost of 1 icecream} \! \times \! \text{Number of icecreams} \\ & \!=\! 25
\! \times \! 3 \\ & \!=\! 75 \\ \end{align}\]
Finally, we have the cost of \(3\) icecreams.
In unitary method, the value of many things is given and we need to either find the value of more or less things.
In order to do that, we must first find the value of one thing by division and then find the value of more or less things by multiplication.
Let’s get back to the stationery shop problem we saw in the What is Unitary Method section above.
We know the cost of \(2\) notebooks is \(\text{Rs.}\;90\).
Now, let’s find the cost of \(5\) notebooks.
STEP 1:
First, we will find the cost of \(1\) notebook.
\[\begin{align}&=\frac{\text{Total cost of books}}{\text{Total number of books}}\\&=\frac{90}{2}\\&=45\end{align}\]
STEP 2:
Now, we will find the cost of \(5\) notebooks.
\[\begin{align}&\!=\!\text{Cost of 1 book}\! \times\! \text{Number of books}\\&\!=\!45 \!\times\! 5\\&\!=\!225\end{align}\]
 The value of many quantities is found by multiplying the value of one quantity with the number of quantities.
 The value of one quantity is found by dividing the value of many quantities by the number of quantities.
Unitary Method to Solve Problems
Unitary Method: Ratio and Proportion
Unitary method in maths is also used to find the ratio between two quantities.
Consider the following situation.
A contractor employed two men, Ram and Shyam, to work in his factory and paid them daily wages.
Ram is paid \(\text{Rs.}\;150\) and Shyam is paid \(\text{Rs.}\;110\) for each day's work.
Ram saves \(\text{Rs.}\;800\) per month and Shyam saves \(\text{Rs.}\;500\) per month.
Can you find the ratio of their monthly expenditure?
Let’s find their monthly income by using the unitary method.
Ram’s wages for one day \(= \text{Rs.} \;150\)
Ram’s wages for one month
\[\begin{align}&= \text{Rs. } (150 \times 30)\\&= \text{Rs. }4500\end{align}\]
Similarly, Shyam’s wages for one month
\[\begin{align}&= \text{Rs. }(110 \times 30)\\&= \text{Rs. }3300\end{align}\]
Now find their monthly expenditure.
Ram’s monthly expenditure
\[\begin{align}&= \text{Rs. }4500  \text{Rs. }800 \\&= \text{Rs. }3700 \end{align}\]
Shyam’s monthly expenditure
\[\begin{align}&= \text{Rs. }3300  \text{Rs. }500 \\& = \text{Rs. }2800 \end{align}\]
The ratio of their monthly expenditure is given by
\[\begin{align}\frac{\text{Ram’s monthly expenditure}}{\text{Shyam’s monthly expenditure}}&=\frac{3700}{2800}\\&=\frac{37}{28}\end{align}\]

Edwin wants to buy a bottle of ink. He has \(\textbf{Rs. }\bf{200}\) in his pocket. At the stationery shop, he was given two options:
a) Bottle costing him \(\textbf{Rs. } \bf{55}\) for \(\bf{2} \textbf{ Litres}\) b) Bottle costing him \(\textbf{Rs. } \bf{70}\) for \(\bf{3}\textbf{ Litres}\)
Frequently Asked Questions (FAQs)
1. What is the formula for unitary method?
2. What is the unitary method for percentage?
To find the \(100%\) amount or the value of an object, unitary method is used. Consider the following example.
In a hospital, \(10%\) of the monthly consumption of milk of patients is \(1540 \text{L}\). What is the \(100%\) monthly consumption of milk in the hospital.
In this case, the unitary method can be used to find the 1% monthly consumption and then multiply \(100\) by the amount of \(1%\) of monthly consumption of milk.
3. What is the unitary ratio?
Unitary method in maths uses this for comparison. For example, there are \(10\) girls and \(20\) boys in a class.
The ratio of girls to boys is \(1:2\). This is a unitary ratio.