Unitary method concepts are covered in this article. In simple terms, the unitary method is used to find the value of a single unit from a given multiple. Here, the key concepts that are covered in this lesson are segregated as the following:

- What is Unitary Method?
- Example of Unitary Method
- Unitary Method Formula
- Unitary Method Applications
- Unitary Method Speed Distance Time
- Unitary Method For Time and Work
- Unitary Method Worksheet (Questions)

## 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 that you recognize the units and values.

For simplification, always write the things to be found 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 much kilometre 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.

## Applications of Unitary Method

The unitary method finds its practical application everywhere ranging from problems of speed, distance, time to problems related to calculating the cost of materials. Let us take unitary method problems for speed distance time and for time and work.

### Unitary Method Speed Distance Time

**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 will be = 1/15

Similarly, B’s 1 day of work will be = 1/10

Now, total work done by A and B in 1 day will be = 1/15 + 1/30

Taking LCM(15, 30) we have,

1 day’s work of A and B = (2+3)/30

1 day’s work of (A + B) = â…™

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

### Unitary Method Questions

- 12 workers finish a job in 20 hours. How many workers will be required to finish the same work in 15 hours?
- If the annual rent of a flat is Rs. 3600, calculate the rent of 7 months.
- If 56 books weigh 8 Kg, calculate the weight of 152 books.
- If 5 cars can carry 325 people, find out the total number of people which 8 cars can carry.
- 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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