Unitary Method

Unitary Method


Unitary method is a popular method in mathematical calculation. This method helps us to find the value of unit quantity from the gross value, and from the value of that unit quantity, we can find the value of the required quantity.



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For the calculation of unit value, we have to either divide or multiply for the direct or indirect variation quantities. And then, we find the required number of quantities by multiplying or dividing accordingly.


Before we proceed to the unitary method, let us have an idea about direct variation and indirect variation.



Direct variation


If two quantities are so related that the increase or decrease in one causes the corresponding increase or decrease in the other, they are said to be in direct variation. Let us take an example of no. of copies and their cost:

 

Table of number of copies and their cost.

Above table shows that if the number of copies increases the total cost also increases. So the number of copies and their cost are in direct variation. To find the unit value for such quantities we have to divide the gross value by the number of quantities. And then, we have to multiply the unit value with the required number of quantities to find the required value. For example:


If the cost of 5 copies is Rs. 250, find the cost of 8 copies.


Solution: Here,


The cost of 5 copies is Rs. 250.     ∴	The cost of 1 copies  is  Rs. 250/5     ∴ The cost of 8 copies  is  Rs. 250/5 × 8 = Rs. 400


The cost of 8 copies is Rs. 400.  


 

Indirect variation


If two quantities are so related that the decrease or increase in one causes the corresponding increase or decrease in the other is called indirect variation. Let us take an example of the number of men and their working days:


Table for number of men and their working days.


Above table shows that if the number of men increases the working days decreases. So the number of men and working days are in indirect variation. To find the unit value for such quantities we have to multiply the gross value by the number of quantities. And then, we have to divide the unit value by the required number of quantities to find the required value. For example:


If 4 men can do a work in 5 days, in how many days 10 men can do the same work?


Solution: Here,


4 men can do a work in 5 days.     ∴ 1 men can do a work in 5×4 days.     ∴ 10 men can do a work in  (5 × 4)/10 days = 2 days


10 men can do the same work in 2 days.


       

Worked Out Examples

 

Example 1: If 10 kg of mangoes cost Rs. 500 then what will be the cost for 15 kg?


Solution: Here,


The cost of 10 kg mangoes is Rs. 500.     ∴ The cost of 1 kg mangoes is Rs.  500/10     ∴ The cost of 15 kg mangoes is Rs. 500/10 × 15  = Rs. 750

15 kg mangoes cost Rs. 750.


 

Example 2: The price of 20 books is Rs. 3000. How many books can be bought for Rs. 1950?


Solution: Here,


Rs. 3000 is the cost of 20 books.     ∴ Re.   1    is the cost of  20/3000 books.     ∴ Rs. 1950 is the cost of  20/3000 × 1950 books  = 13 books.


13 books can be bought for Rs. 1950.


 

Example 3: If ¾ of a man’s income is Rs. 3000, what will be ¼ of his income?


Solution: Here,


3/4 of a man’s income is Rs. 3000.     ∴ 1 of a man’s income is Rs. 3000/(3/4)     ∴ 1/4 of a man’s income is Rs. (3000×1/4)/(3/4)  = Rs. (3000 × 4)/(3 × 4)  = Rs. 1000


¼ of his income is Rs. 1000.


 

Example 4: If a work can be completed by 20 people in 45 days. How long will it take to complete the same work by 15 people?


Solution: Here,


20 people can complete a work in 45 days.     ∴ 1 person can complete a work in 45×20 days.     ∴ 15 people can complete a work in  (45×20)/15 days  = 60 days

It will take 60 days to complete the same work by 15 people.



Example 5: A garrison of 800 men has provision for 120 days. How many men should be added to finish the provision in 100 days?


Solution: Here,


For 120 days, there is provision for 800 men.     ∴ For 1 day, there is provision for 800×120 men.     ∴ 100 days, there is provision for  (800×120)/100 men.  = 960 men.


960 – 800 = 160 men should be added to finish the provision in 100 days.

 

 

Do you have any questions regarding the unitary method?

You can ask your questions or problems here in the comment section below.

2 comments:

  1. two pipes P and Q can fill a tank in 24 minutes and 30 minutes respectively. both pipes are opened together and the first pipe is closed after 8 minutes. after how many minutes the tank will be filled?

    ReplyDelete