Unitary Method with Examples and FAQs

What is the unitary method?

The unitary method is a method of calculating the value of a single unit from a given value. It can further be used to calculate the value of the required number of units. This is the basic and most commonly used method for calculation in many math problems.

For example,

The cost of a dozen of bananas is ₹36. what will be the cost of 7 bananas?

Solving by unitary method:

Given cost of a dozen of bananas is ₹36

Then cost of 1 banana =\frac{\text { Total cost of bananas }}{\text { Total number of bananas }}=\frac{36}{12}=₹ 3

Therefore the cost of 1 banana \times 7=₹ 3 \times 7=₹ 21

Unitary Method in Ratio and Proportion

This method is commonly used to find ratios between two given quantities.

For example:

A and B are employees of a company. A’s salary per annum is ₹2,40,000 and that of B is ₹22000 per month. A saves ₹5000 a month a B saves ₹12000 a month. What is the ratio of their monthly expenditure?

A’s salary is ₹2,40,000 per annum, i.e., for 12 months.

∴ A’s monthly salary 

=\frac{\text { Total salary }}{\text { Number of months }}

=\frac{240000}{12}

=20000

Therefore, A earns ₹20,000 per month.

A’s monthly income is ₹20,000 and savings is ₹5,000.

∴ A’s monthly expenditure = Monthly income – Monthly savings 

                                                = ₹20,000 – ₹5,000

                                                = ₹15,000

B’s monthly income is ₹22,000 and savings is ₹12,000.

∴ B’s monthly expenditure = Monthly income – Monthly savings 

                                                = ₹22,000 – ₹12,000

                                                = ₹10,000

∴ The ratio of their monthly expenditure is given by,

\frac{A^{\prime} s \text { monthly expenditure }}{B^{\prime} s \text { monthly expenditure }}=\frac{15,000}{10,000}=\frac{3}{2}

Types of Unitary Method

The calculations involved in the unitary method can have two variations, which are:

(1) Direct Variation

In the case of direct variation if one quantity increases the other quantity will also increase.

For example, if the number of items purchased is increased then in that case the cost will also increase. Here, the number of items purchased and the cost of items are in a relationship with one another directly, i.e., if one increases the other will also increase.

(2) Indirect Variation

In the case of indirect variation if one quantity increases the other quantity will decrease.

For example, suppose a car is moving at a given speed to reach a fixed distance. Suddenly if the speed of the car is increased then the distance can be reached in a lesser span of time. Here, the speed of the car and the travelling time are in a relationship with one another indirectly, i.e., if one increases the other will decrease.

Applications of Unitary Method

The unitary method can be used to solve a lot of mathematics problems in day-to-day life. Some of the ways in which the method is used are:

1. It can be used in evaluating the price of an item when the price of a number of items is given.
2. It can be used to solve business problems by calculating profit and loss.
3. It is even used in calculating the percentage of a quantity.
4. It finds use in calculating the amount of work and time taken to complete the work.

Examples

Example 1: A car is travelling at a speed of 120 kmph. What is the distance covered in 2 hours?

Solution: 

We know,

Distance = Speed × Time

Given: Speed = 120 kmph

⇒ The distance travelled by car in an hour is 120 km.

∴ the distance covered by car in 2 hours = distance covered by a car in an hour × 2

⇒ Required distance covered = 120 × 2 = 240 km

Therefore, the car covered a distance of 240 km in 2 hours.

Example 2: Anushka goes to a stationery shop to buy some pencils. The shopkeeper informs her that the cost of 5 pencils is ₹15. Calculate the cost of 20 pencils by the unitary method.

Solution:

It is given that the cost of 5 pencils is ₹15.

\Rightarrow \text { cost of } 1 \text { pencil }=\frac{\text { Total cost of pencils }}{\text { Total number of pencils }}=\frac{15}{5}=₹ 3

Now, we will calculate the cost of 20 pencils.

Cost of 20 pencils = Cost of 1 pencil × Number of pencils = 3 × 20 = ₹60

Therefore, the cost of 20 pencils is ₹60.