Unitary Method

In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit. This method is majorly used for ratio and proportion concept.

What is Unitary Method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values be?

Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important to recognize the units and values.

For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side. In the above problem, we know the amount of the number of apples and the value of the apples is unknown. It should be noted that the concept of ratio and proportion is used for problems related to this method.

Example of Unitary Method

Consider another example; a car runs 150 km on 15 litres of fuel, how many kilometres will it run on 10 litres of fuel?

In the above question, try and identify units (known) and values (unknown).

Kilometre = Unknown (Right Hand Side)

No of litres of fuel = Known (Left Hand Side)

Now we will try and solve this problem.

15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 x 10 = 100 km

The car will run 100 kilometres on 10 litres of fuel.

Unitary Method in Ratio and Proportion

If we need to find the ratio of one quantity with respect to another quantity, then we need to use the unitary method. Let us understand with the help of examples.

Example: Income of Amir is Rs 12000 per month, and that of Amit is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month, find the ratio of their savings.

Solution: Savings of Amir per month = Rs (12000 – 9960) = Rs 2040

In 12 month Amit earn = Rs.191520

Income of Amit per month =  Rs 191520/12 = Rs. 15960

Savings of Amit per month = Rs (15960 – 9960) =  Rs 6000

Therefore, the ratio of savings of Amir and Amit  = 2040:6000 = 17:50

Types of Unitary Method

In the unitary method, the value of a unit quantity is calculated first to calculate the value of other units. It has two types of variations.

1. Direct Variation
2. Inverse Variation

Direct Variation

In direct variation, increase or decrease in one quantity will cause an increase or decrease in another quantity. For instance, an increase in the number of goods will cost more price. 

Also, the amount of work done by a single man will be less than the amount of work done by a group of men. Hence, if we increase the number of men, the work will increase.

Indirect Variation

It is the inverse of direct variation. If we increase a quantity, then the value of another quantity gets decrease. For example, if we increase the speed, then we can cover the distance in less time. So, with an increase in speed, the travelling time will decrease.

Applications of Unitary Method

The unitary method finds its practical application everywhere ranging from problems of speed, distance, time to the problems related to calculating the cost of materials.

• The method is used for evaluating the price of a good.
• It is used to find the time taken by a vehicle or a person to cover some distance in an hour.
• It is used in business to determine profit and loss.

Unitary Method Speed Distance Time

Let us take unitary method problems for speed distance time and for time and work.

Illustration: A car travelling at a speed of 140 kmph covers 420 km. How much time will it take to cover 280 km?

Solution: First, we need to find the time required to cover 420 km.

Speed = Distance/Time

140 = 420/T

T = 3 hours

Applying the unitary method,

420 km = 3 hours

1 km = 3/420 hour

280 km = (3/420) x 280 = 2 hours

Unitary Method For Time and Work

Example: “A” finishes his work in 15 days while “B” takes 10 days. How many days will the same work be done if they work together?

Solution:

If A takes 15 days to finish his work then,

A’s 1 day of work = 1/15

Similarly, B’s 1 day of work = 1/10

Now, total work is done by A and B in 1 day = 1/15 + 1/10

Taking LCM(15, 10), we have,

1 day’s work of A and B = (2+3)/30

1 day’s work of  (A + B) = ⅙

Thus, A and B can finish the work in 6 days if they work together.

Unitary Method Questions

1. 12 workers finish a job in 20 hours. How many workers will be required to finish the same work in 15 hours?
2. If the annual rent of a flat is Rs. 3600, calculate the rent of 7 months.
3. If 56 books weigh 8 Kg, calculate the weight of 152 books.
4. If 5 cars can carry 325 people, find out the total number of people which 8 cars can carry.
5. Rakesh completes 5/8 of a job in 20 days. How many more days will he take to finish the job at his current rate?

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