Today I am going to discuss Unitary Method under this section. Unitary method is part of Ratio and Proportion chapter. This topic has various applications and can be used in many other topics like Time and Work. It involves basic calculations and generally includes two types of proportions: Direct proportion and Indirect proportion. In unitary method question we just need to identify whether it is a direct proportionality or indirect proportionality. Rest is very simple task.
Unitary Method: Finding value of one unit first. Then finding value of required number of units. Therefore, Unitary method comprises two following steps:
Step 1 = Find the value of one unit.
Step 2 = Then find the value of required number of units.
For example: If 1 mango = Rs 5, then 5 mangoes = 5*5 = Rs.25
Problem1: If 6 note books costs Rs.45, then how much 8 note books costs?
Solution: 6 notebooks = Rs.45
1 notebook = Rs.45/ 6 ( unit price)
8 notebooks = Rs. (45/ 6)*8 = Rs.60
Problem 2: 85 students consume a particular stock in 60 days. How many days 51 students will take to consume that stock?
Solution: This is a case of inverse proportion.
More students, less days ; Less students, more days.
85 students consume in 60 days. Lets write it as:
85 students = 60 days
Converting it into a unit
1 student = 85 * 60 days ( less students, more days)
Therefore, 51 students = (85 * 60)/ 51 days
⇒ 51 students = 5100/ 51 = 100 days
⇒ 51 students consume that stock in 100 days.
Problem 3: 5 workers can complete work in 20 days. In how many days, 10 workers can complete the work?
Solution: This is a case of inverse proportion.
More workers, less days; less workers, more days
5 workers complete work in 20 days
i.e. 5 workers = 20 days
1 worker = 20 * 5 days (less workers, more days)
Therefore,10 workers = 110/ 10 = 10 days
⇒ 10 workers take 10 days to complete work.
Solution: In problems related to three variables, we will firstly deal with two variables then with the third.
According to question, 40 persons consume 200 kg rice in 30days
Firstly, I'm going to deal with quantity of rice and number of days
40 PERSONS:
200 kg = 30 days
1 kg = 30/ 200 days (Direct proportion)
500 kg = (30/ 200) * 500 = 75 days
Now, i will deal with third variable
1 PERSON:
40 persons = 75 days
1 person = 75* 40 days ( Inverse proportion)
30 PERSONS:
30 PERSONS = (75* 40)/ 30
⇒ 3000/30 = 100 days
Therefore, 30 persons consume 500kg in 100 days.
Problem2: 500 persons consume 100 kg of wheat in 20 days. How many days will 20 persons take to consume 1000 kg rice?
Solution: Do it yourself
Unitary Method: Finding value of one unit first. Then finding value of required number of units. Therefore, Unitary method comprises two following steps:
Step 1 = Find the value of one unit.
Step 2 = Then find the value of required number of units.
For example: If 1 mango = Rs 5, then 5 mangoes = 5*5 = Rs.25
Problems for practice
Problem1: If 6 note books costs Rs.45, then how much 8 note books costs?
Solution: 6 notebooks = Rs.45
1 notebook = Rs.45/ 6 ( unit price)
8 notebooks = Rs. (45/ 6)*8 = Rs.60
Problem 2: 85 students consume a particular stock in 60 days. How many days 51 students will take to consume that stock?
Solution: This is a case of inverse proportion.
More students, less days ; Less students, more days.
85 students consume in 60 days. Lets write it as:
85 students = 60 days
Converting it into a unit
1 student = 85 * 60 days ( less students, more days)
Therefore, 51 students = (85 * 60)/ 51 days
⇒ 51 students = 5100/ 51 = 100 days
⇒ 51 students consume that stock in 100 days.
Problem 3: 5 workers can complete work in 20 days. In how many days, 10 workers can complete the work?
Solution: This is a case of inverse proportion.
More workers, less days; less workers, more days
5 workers complete work in 20 days
i.e. 5 workers = 20 days
1 worker = 20 * 5 days (less workers, more days)
Therefore,10 workers = 110/ 10 = 10 days
⇒ 10 workers take 10 days to complete work.
Problems related to three variables
Problem1: 40 persons consume 200kg rice in 30 days. In how many days will 3 persons consume 500kg rice?Solution: In problems related to three variables, we will firstly deal with two variables then with the third.
According to question, 40 persons consume 200 kg rice in 30days
Firstly, I'm going to deal with quantity of rice and number of days
40 PERSONS:
200 kg = 30 days
1 kg = 30/ 200 days (Direct proportion)
500 kg = (30/ 200) * 500 = 75 days
Now, i will deal with third variable
1 PERSON:
40 persons = 75 days
1 person = 75* 40 days ( Inverse proportion)
30 PERSONS:
30 PERSONS = (75* 40)/ 30
⇒ 3000/30 = 100 days
Therefore, 30 persons consume 500kg in 100 days.
Problem2: 500 persons consume 100 kg of wheat in 20 days. How many days will 20 persons take to consume 1000 kg rice?
Solution: Do it yourself
