The method in which we first find the value of a unit quantity and then use it to find the value of any required quantity is called the unitary method. The unitary method can be used to solve problems related to distance, time speed, and calculating the cost of materials. The unitary method is used for various applications.
The unitary method consists of two type of variations:
- Two quantities are said to be in direct variation if one quantity increases, then the other also increases or when one quantity decreases, the other also decreases.
- Two quantities are said to be inverse variation if,
- On increasing one quantity, the other quantity decreases.
- On decreasing one quantity, the other quantity increases.
Let us consider some examples:
Example 1: The cost of 15 pens is Rs 360, What is the cost of 8 such pens?
Solution:
Cost of 15 pens = Rs, 360.
Cost of 1 pen = Rs. 360/15.
Cost of 8 pen = (360/15) * 8 = Rs 192.
Example 2: 18 men can make 90 identical tables in one day. Find how many men will make 20 such tables in one day?
Solution:
In one day, 90 tables are made by 18 men.
In one day, 1 tables are made by 18/1 men.
In one day, 20 tables are made by (18/1) * 20 men.
Example 3: A car running with uniform speed covers a distance of 96 km in 3 hours. How much distance will the car cover in 5 hours running with the same speed?
Solution:
In 3 hours, car covers 96 km.
In 1 hours, car covers km = (96/3) = 32 km.
In 5 hours, car covers = 32 * 5 = 170 km.
Example 4: A car can travel 360 km consuming 24 litres of petrol. How much petrol will it consume while travelling through a distance of 480 km?
Solution:
The car can travel 360 km consuming 24 litres of petrol.
The car can travel 1 km consuming (24/360)km.
The car can travel 480 km consuming = (24/360) * 480 = 32 litres.