Unitary Method

Unitary Method – Definition

The unitary method is a fundamental concept of Mathematics and makes it convenient to solve various sums. This method generally involves finding the value of a unit in the given terms, using which the value of the given quantity of units can be calculated. The following example will help you understand the terms ‘unit’ and ‘value’. You buy 7 juicy apples from your local grocery shop. The shopkeeper puts up an offer of purchasing 10 apples for Rs 100. In this situation, the ‘units’ are the apples and the ‘value’ is the price of the apples. 

It is important to recognize and familiarize the terms of units and values when using the unitary method in your sums.

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A simple tip is to write the values to be calculated on the right-hand side and known values on the left-hand side. The problem present above clearly indicates the number and total price of apples as unknown. At this point, the use of ratio and proportions come into the picture.

Concept Behind Unitary Method

The unitary method concept helps us to pick out a single value from a multiple set of values having different properties. For Instance, the price of 40 pens is Rs. 400, how do we calculate the price of a single pen?

This can be done using the unitary method. After finding the value of a single pen, we calculate the value of the required number of pens. This is done by multiplying the value of the single unit by the given number of units. 

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Example of Unitary Method Problems

While going through a variety of sums to understand the unitary method, be sure to pay attention to the items in the given set of data. Given below are some of the common unitary method sums.

Let us consider the following example. A car runs 150 km on 15 liters of fuel, how many kilometers will it run on 10 liters of fuel?

First, we try to identify our quantities, 

Here, the units are known, however, the values are unknown.

Kilometer = Unknown (Place in the Right Hand Side)

No of liters of fuel = Known (place in the Left Hand Side)


15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 х 10 = 100 km 

Therefore, the car can run 100 kilometers on 10 liters of fuel.

Unitary Method in Time and Work

The unitary method uses the properties of time and works in the relevant numerical problems.

Let us consider the following example. Desmond finishes his work in 15 days while Betty takes 10 days. Find the number of days it will take them to complete the same work together?

If Desmond takes 15 days to finish his work then,

Desmond’s 1 day of work =1/15

Betty’s 1 day of work = 1/10

Now, the total work is done be Desmond and Betty in 1 day = 1/15 + 1/10

Taking the LCM (15, 10),

1 day’s work of Desmond and Betty = 2+3/30

1 day’s work of (Desmond + Betty) = 1/6

Thus, if Desmond and Betty work together, they can complete the work in 6 days. 

 Ratio and Proportion in Unitary Method

The concepts of ratio-proportion and unitary method are inter-linked. The majority of the sums in ratio and proportion exercises are based on fractions. A fraction is represented as a:b. The terms ‘a’ and ‘b’ can be any two integers.

To find the ratio of one quantity for another requires the use of the unitary method.

Consider the following example. The income of Ajay is Rs 12000 per month, and that of Bob is Rs 191520 per annum. If the monthly expenditure for each is Rs 9960 per month, express their savings in terms of ratios.

The savings of Ajay per month = Rs (12000 - 9960) = Rs 2040

In 12 months, Bob earns = Rs.191520

The Income of Bob per month = Rs 191520/12 = Rs. 15960

The savings of Bob per month = Rs(15960 - 9960) = Rs 6000

Therefore, the ratio of savings of Ajay and Bob = 2040 : 6000 = 17 : 50

FAQs on Unitary Method

1. What are the Two Types of Unitary Methods?

The unitary method greatly relies on the concept of ratio and proportions. But, depending on the value and quantity of a unit to be primarily calculated, there are two types of variations found. 

Direct Variation - There is an increase or decrease in one quantity and this reflects on the increase or decrease in the next quantity. 

For example, the increase in the number of goods will hike up the price. The amount of work done by a group of men is relatively higher than that of a single man. 

Inverse Variation - The inverse of direct variation results in inverse variation. The quantity of two sets is inversely proportional, that is, one increase results in the decrease of the other.

For instance, when speed increases, more distance is covered in less time. 

2. What are the Applications of the Unitary Method?

The practical applications of the unitary method are vast. It is used for solving complex problems in Mathematics. This involves the sums of speed, distance, time, work, ratio, and proportions. To some extent, it aids in the realm of Finance as well. It can be used to calculate the cost of goods or to establish their pricing based on the local or global market trends. 

It can be used to determine the profit and loss attained by a company. The most common problems solved by the unitary method uses the concept of distance covered and time taken by different transportation systems.

When you buy things like veggies in your daily life, the merchant always specifies the wholesale rates. Let's say you spend 250 rupees on 5 kilograms of rice. How can you determine the price of a unit kilogram of rice? The unitary approach is the answer to this. Furthermore, given the cost of a single unit, you may use this to compute the price of numerous units. 

Let us learn about the unitary technique because of its importance in our daily lives.

A single or individual unit is referred to as unitary. As a result, the goal of this method is to determine values about a single unit. For example, if a bike travels 60 kilometres on two litres of petrol, you can use the unitary technique to calculate how many kilometres it will go on one litre of petrol.

The unitary method, in other words, is the process by which we determine the value of one unit and then utilise it to determine the value of numerous units. Let's look at an example of how the unitary approach is used:

Assume, Rahul spends 120 Rs on a dozen bananas. This implies that 12 bananas are worth 120 rupees. 1 banana costs 120/12 = 10 rupees. As a result, a single banana costs ten rupees. Let's say you need to calculate the cost of 24 bananas. This can be done as follows: 1 banana costs 10 rupees; 24 units will cost 240 rupees.

In other words, if you are given the value of several goods, you simply divide the total value by the number of units to get the value of one unit. The unitary technique is what it sounds like.

Let's now solve some questions to understand the concept of the unitary method. 

3. The price of ten pens is Rs. 50. Find the maximum number of pens that can be bought for 100 Rs.

The cost of ten pens is estimated to be 50 rupees. As a result, the price of a pen is 5 rupees. Now,

The number of pens that can be purchased for 100 rupees equals to 20.

4. What is the unitary method's formula?

If we have the value of numerous objects with us, we can simply divide the total value by the number of units to get the value of one unit, which is called the unitary technique.

5. What is the percentage unitary method?

The unitary approach can be used to find 100 percent of an amount given a percentage of it. For example, if 50% of a sum of money is Rs. 40, then its 100% is (100/50) × 40 = Rs. 80

6. What is the unitary ratio?

When one side of a ratio is one, the ratio is referred to as a unitary ratio. This comes in handy when comparing two things.

7. How is the unitary method defined in terms of mathematics? 

The unitary method is a method of determining the answer to a problem by first determining the value of a single unit and then multiplying the single unit value by the essential value. This technique, on the other hand, is useful for determining the value of a unit from the value of a multiple, and thus the value of a multiple. 

8. How can I understand the concept of the unitary method?

The concept of the unitary method is very easy to understand as you first have to find the value of a unit from a given problem. In the above article, we have provided a lot of examples that will help you to understand the concept of the unitary method very easily. You will also find the definitions of all the terms that are related to the unitary method. 

9. What are the various examples where the unitary method can be applied?

The unitary method can be applied to two sets of examples viz; examples revolving around indirect variations and examples revolving around direct variations. In both types of variations, you can find the value of the single unit. To find the value of that single unit, you first have to figure out whether the problem is related to direct variation or indirect variation.