# Unitary Method

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 1 What is Unitary Method? 2 Different Types of Unitary Method 3 Example of Unitary Method 4 Important Notes 5 Unitary Method to Solve Problems 6 Challenging Questions on Unitary Method 7 Practice Questions 8 Maths Olympiad Sample Papers 9 Frequently Asked Questions (FAQs)

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## 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 vice-versa.

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 vice-versa.

For example:

Increasing the speed of the car will result in covering a fixed distance in lesser time. Help your child score higher with Cuemath’s proprietary FREE Diagnostic Test. Get access to detailed reports, customized learning plans, and a FREE counseling session. Attempt the test now.

## Example of Unitary Method

Ria went to an ice-cream parlour and bought $$5$$ ice-creams.

She paid $$\text{Rs.}\;125$$ to the shopkeeper.

What would be the cost of $$3$$ ice-creams? 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 $$5$$ ice-creams.

$$5$$ ice-creams cost $$\text{Rs.}\;125$$.

STEP 1:

Let’s find the cost of $$1$$ ice-cream.

In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream:

\begin{align}&=\frac{\text{Total cost of ice-creams}}{\text{Total number of ice-creams}}\\&=\frac{125}{5}\\&=25\end{align}

Therefore, the cost of $$1$$ ice-cream is $$\text{Rs.}\;25$$.

STEP 2:

To find the cost of $$3$$ ice-creams, multiply the cost of $$1$$ ice-cream with the number of ice-creams.

Cost of 3 ice-creams:

\begin{align} &\!= \!\text{Cost of 1 ice-cream} \! \times \! \text{Number of ice-creams} \\ & \!=\! 25 \! \times \! 3 \\ & \!=\! 75 \\ \end{align}

Finally, we have the cost of $$3$$ ice-creams.

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}

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