Table of contents  
Unitary Method  
Types of Unitary Method  
Steps to use Unitary Method  
Unitary Method in Ratio and Proportion  
Uses of Unitary Method 
Definition of Unitary Method : Unitary Method is a mathematical process to calculate the value of a single unit from the value of multiple units and the value of multiple unit rate from the value of a single unit.
Example 1: If we have been provided with data where it is said that 3 students can together complete a group project within 5hrs, and we need to calculate how many hours it is required to complete that project if the group has 5 students.
Sol: Here we have a value of a certain quantity i.e., 3 students need 5 hrs to complete, and we need to find the value for a desired quantity i.e., number of hours required by 5 students.
So we can use the Unitary Method here to get the desired value.
So, Number of hours taken by 1 student = 5/3 = 1.6667.
Therefore, Number of hours taken by 5 students = 1.6667×5 = 8.3335
There are two types of variation that we see while using Unitary Method under coefficient of variation.
The steps to use the unitary method are mentioned below.
Example 2: We have been given the cost of buying 10 balls which is Rs 95, and we need to calculate the cost of 7 balls.
Sol: So according to the above mentioned step 1 we first find the value unit quantity i.e, cost of buying one ball = 95/10 = Rs 9.5
Now we can calculate the value of required quantity mentioned in step 2 by multiplying the cost of 1 ball with the obtained value, i.e., 9.5 x 7 = Rs 68.5
Thus we get the cost of 7 balls using unitary method which is Rs 68.5
The Unitary Method is also used to find the ratio of one quantity with respect to another quantity. The concepts of ratioproportion and unitary method are very much interrelated. The sums of 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.
Example 3: The Income of Harish is Rs 20000 per month, and that of Shalini is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9000 per month, find the ratio of their savings.
Sol:
Unitary Method has vast use in solving various problems in our daytoday life. The main uses are listed below.
Example 4: The cost of 2 notebooks is Rs. 90. Calculate the cost of 10 notebooks.
Sol: We have the given quantity as 2 and the value of these 2 quantities is Rs. 90.
First we find the value of 1 quantity,
Next we calculate the value of 10 notebooks,
Cost of 10 notebooks = Cost of 1 notebook × Number of 10 books = 45 × 10 = Rs 450
Thus we get the cost of 10 notebooks i.e., Rs. 450
Example 5: Which of the following options is cost effective?
(i) Bottle A costs Rs.55 for 2 Liters
(ii) Bottle B costs Rs.70 for 3 Liters
Sol: We can use the Unitary Method to choose the cost effective option. We can find the cost of 1 liter which will help us to identify the cost effective bottle.
(i) Cost of 1 liter = 55/2 = Rs. 27.5
(ii) Cost of 1 liter = 70/3 = Rs. 23.3
As the cost of 1 liter from bottle B is less than the cost of 1 liter from bottle A.
Thus bottle B is more cost effective.
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