The basic understanding of the concept of unitary method is very important because from school level to any type of competition level unitary concept questions are always on your way. This Method is important and always preferred.
What is Unitary Method?
The method in which the value of a unit quantity is first calculated to get the value of any quantity.
We come across two types of variations:-
Type of variations
Condition
Examples
Direct variation
Increase in one quantity causes an increase in the other quantity and decrease in one quantity causes decrease in the other quantity.
(I)With more money, more articles can be bought. (II)With a greater speed, the larger distance can be covered at the same time. (III)With less number of men, less work can be done in same time, etc.
Inverse variation
Increase in one quantity causes a decrease in the other quantity and decrease in one quantity causes an increase in the other quantity.
(I)With greater speed, less time will be taken to cover the same distance. (II)With less number of men, more days are required for the same work, etc.
Unitary Method in Maths
Consider the following examples
1. If the cost of 15m cloth= rs300 Cost of 1m cloth=rs 300/15 = rs20 And the cost of 10m cloth=10 x rs20= rs200
2. If 15 men can do some work in 300 days 1 man can do the same work in 300 x 15days=4500 days And 10 men will do it in 4500/10 days = 450 days.
In part 1, given above, the cost of 1m cloth is first obtained from the given cost of 15m and then the cost of 10m is found.
In the same way, in part 2, given above, the number of days taken by 1 man is first calculated from the number of days by 15 men and then the number of days taken by 10 men is obtained.
Unitary Method Formula
Example1: A man earns R 400 in 10 days. How much will he earn in 28 days? Answer: Note: For Solving problems, the sentences (statements) should be framed in Such a way that, whatever is to be found is Written at the end of the statement.
Arrow Method Formula:
Steps:
In the case of inverse variation, the arrow for this Column must be in the direction opposite to the direction of the first arrow.
Since here we have the case of direct variation, therefore, for both the columns arrows must be in the same direction.
Unitary Method Example
Example2- 0.75-meter cloth costs rs 45. What will be the cost of 0.6m of the same cloth?
Example3- 4 men can do a piece of work in 5 Days.How many men will do it in 4 days?
Example4- With a speed of 60km/hr, it takes 4 hours to cover a certain distance. What should be the speed if the same journey is to be completed in 3 hours?
Problems For Practice
6 books weigh 1.260kg.How many books will weigh 3.150kg?
8 men complete a work in 6 hours. In how many hours will 12 men complete the same work?
A typist takes 80 minutes to type 24 pages. How long will he take to type 87 pages?
A truck uses 20 liters of diesel for 240 km.How many liters will be needed for 1200km?
If 3 dozen eggs costs 90rs find the cost of 3 score eggs?(1 score=20)
This is all about the Basic Concept, Formula, Example, Problems.
We come across two types of variations:-
Note: For Solving problems, the sentences (statements) should be framed in Such a way that, whatever is to be found is Written at the end of the statement.
Note: For Solving problems, the sentences (statements) should be framed in Such a way that, whatever is to be found is Written at the end of the statement.
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