Revision Notes on Unitary Method
Learning Goal
- Unitary Method
- Types of Unitary Method
- Unitary Method in Ratio and Proportion
- Unitary Method for Speed Distance Time
- Unitary Method for Time and Work
Unitary Method
A method in which the value of unit quantity is first obtained to find the value of a required quantity is called unitary methods.
Types of Unitary Method
- Direct Variation
- Inverse Variation
Direct Variation (Direct proportion)
In direct variation, increase or decrease in one quantity will cause an increase or decrease in another quantity.
Ex- increase in the number of goods than cost of goods also increases
increase the number of men, the work will increase.
Indirect Variation (Inverse proportion)
It is the inverse of direct variation.
If we increase a quantity, then the value of another quantity gets decrease.
Ex- increase in speed, the travelling time will decrease.
Note- Unitary Method in Ratio and Proportion
Methods of solving
Try and identify quantity (known) and values (unknown). Now write it in following way-
Kilometre = Unknown (Right Hand Side)
No of litres of fuel = Known (Left Hand Side)
Example
A car runs 150 km on 15 litres of fuel, how many kilometres will it run on 10 litres of fuel?
Here, Kilometre = Unknown (Right Hand Side)
No of litres of fuel = Known (Left Hand Side)
Solving By Ratio and Proportion Methods
Hence car runs 100 Km in 10 litres.
Example
A car runs 150 km on 15 litres of fuel, how many fuels will it take to run 200 km?
Here, fuel = Unknown (Right Hand Side)
No of Kilometre = Known (Left Hand Side)
Unitary Method in Ratio and Proportion
If we need to find the ratio of one quantity with respect to another quantity, then we need to use the unitary method. Let us understand with the help of examples.
Example: Income of Amir is Rs 12000 per month, and that of Amit is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month, find the ratio of their savings.
Solution: Savings of Amir per month = Rs (12000 – 9960) = Rs 2040
In 12 month Amit earn = Rs.191520
Income of Amit per month = Rs 191520/12 = Rs. 15960
Savings of Amit per month = Rs (15960 – 9960) = Rs 6000
Therefore, the ratio of savings of Amir and Amit = 2040:6000 = 17:50
Unitary Method Speed Distance Time
Let us take unitary method problems for speed distance time and for time and work.
Illustration: A car travelling at a speed of 140 kmph covers 420 km. How much time will it take to cover 280 km?
Solution: First, we need to find the time required to cover 420 km.
Speed = Distance/Time
140 = 420/T
T = 3 hours
Applying the unitary method,
420 km = 3 hours
1 km = 3/420 hour
280 km = (3/420) x 280 = 2 hours
Unitary Method For Time and Work
Example: “A” finishes his work in 15 days while “B” takes 10 days. How many days will the same work be done if they work together?
Solution:
If A takes 15 days to finish his work then,
A’s 1 day of work = 1/15
Similarly, B’s 1 day of work = 1/10
Now, total work is done by A and B in 1 day = 1/15 + 1/10
Taking LCM(15, 10), we have,
1 day’s work of A and B = (2+3)/30
1 day’s work of (A + B) = ⅙
Thus, A and B can finish the work in 6 days if they work together.
Unitary Method Questions
- 12 workers finish a job in 20 hours. How many workers will be required to finish the same work in 15 hours?
- If the annual rent of a flat is Rs. 3600, calculate the rent of 7 months.
- If 56 books weigh 8 Kg, calculate the weight of 152 books.
- If 5 cars can carry 325 people, find out the total number of people which 8 cars can carry.
- Rakesh completes 5/8 of a job in 20 days. How many more days will he take to finish the job at his current rate?