# Unitary Method

The unitary method, in essence, is all about finding the “**per unit value**”. The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. This thus becomes important in more advanced ideas like determining the amount of time, resources or capital required for certain types of problems, often which have their own constraints.

Let’s try and understand this using an example,

The cost of 5 apples is ₹ 30.

The cost of 1 apple is = 30 ÷ 5 = ₹ 6

The cost of 7 apples = 7 x 6 = ₹ 42

The unitary method forms an important part of more advanced mathematical concepts such as optimization and operations research where problem statements are converted into equations and then solved.

For example, you go to a supermarket and see two offers on the same product (say sugar) from 2 different brands:

- Brand A is offering 500g sugar for Rs. 80
- Brand B is offering 750g of sugar for Rs. 10

Which brand is the better deal? With Unitary method, your life would be made extremely simple!

## Speed distance and time

Suppose you travel in a car from Chennai to Bengaluru. You reach Bengaluru in 7 hours.

The distance between Chennai and Bengaluru is 350 Km.

The time taken to travel is 7 hrs.

The distance covered in 1 hour = 350 km/7 hr

This measure of distance per unit of time is called **speed**.

**Formula:** Speed is calculated as distance/time taken.

In this case the speed of the car is 50 km/ hr.

(In this example, we assume that the car was travelling at the same speed through its journey. Similarly, in the next set of questions we will assume that the speed remains constant throughout the journey.)

## Tips and Tricks

- Not always do you have to use the unitary method to find the per-unit value.

If 32 items cost Rs 40. How much will 12 items cost?

Here finding the cost of each item as per the unitary method will be tedious (32 ÷ 40).

Instead use the trick from equivalent fractions to find an equivalent fraction to \(\begin{align} 32\over 40\end{align}\) with numerator 12:

This says you’ll get 12 items per Rs 15. That is, the cost of 12 items is Rs 15.

## Test your knowledge

- Hari earned ₹4000 for 8 days of work. He was paid an equal amount each day. How much did he earn per day?
- Dan can cycle 35 km in 4 hours. How many kilometers can he cover in 1 hour, if he covers the same distance every hour?
- A bakery sells 69 buns in 3 days and 56 cakes in 4 days. An equal number of buns were sold each day. Similarly, an equal number of cakes were sold each day. Which item was sold more in a day?