Unitary Method


The unitary method is one of the most important processes used to calculate problems with variable quantities. It is a technique in elementary algebra, which involves changing one of the variables into a single unit. The term “unitary,” itself reveals what it is all about.

In Depth

Unitary method has several uses in our daily life like when we talk about speed, rate or percentage, we invariably relate to unitary method. For instance, when we calculate the average speed of a car, that has traveled 130 kilometers in 2 hours, we end up calculating the distance traveled by the car in 1 hour. After calculating we find, assuming the car has traveled in uniform velocity the speed of the car was 65 kilometers per hour. Therefore, we are altering one of the quantities (time in this case) into a unit.

Another suitable example would be ‘rate’. Whenever, we talk about rate, we mean to say the cost of a unit quantity of a particular material. For instance, when we say the rate of oil is $200, we mean to say that it is the cost of per gallon or per liter. Therefore, unitary method is an integral part of our daily life.

To calculate the percentage of a certain quantity, unitary method is also used. For instance, if you are asked to calculate 9% of 1000 kilograms, all you need to do is to find out the amount equivalent to 1% of 1000 kg. Once it is calculated then you can easily find out 9% of 1000 kg by multiplying the result of 1% by 9. In most of the cases, the quantities are directly proportional to each other but in case of man and work they are inversely proportional to each other. For instance, if a piece of work is completed in 5 days by 2 men then it will be obviously completed earlier if the work is done by more number of men. Therefore, it proves that they are inversely related to each other.


There are numerous examples, which prove that unitary method is used in our every day life. The concept of unitary method can be better understood with some more examples, like:

  1. Suppose, a car travels 90 miles in 3 hours. Calculate the speed of the car.
    • Calculating the speed of the car means we have to find the average distance covered by the car in 1 hour.
    • Distance traveled by the car in 3 hours = 90 miles.
      Distance traveled by the car in 1 hour = 90/3 miles.
      Distance traveled y the car in 1 hour = 30 miles.
    • Therefore, speed of the car is 30 miles/hour.
  2. Another example would be, if you were asked to return 6% of the $500 as interest then what is the amount of interest you have to pay?
    • Let’s take $500 as 100%
      100% of the total money = $500
      By unitary method, 1% of the total money = 500/100
      6% of the total money = 500/100 x 6
    • Therefore, 6% of the total money = $ 30
  3. Find the rate of edible oils if the cost of 200 liters is $400.
    • Cost of 200 liters of edible oil = $400
      Cost of 1 liter of edible oil = $400/200
      Cost of 1 liter of edible oil = $2
    • Therefore, the rate of edible oil is $2/liter.
  4. A work is completed by 10 men in 50 days. How long will 25 men take to complete the work?
    • Total work is completed by 10 men in = 50 days
      Total work is completed by 1 man in =  50 x 10 days = 500 days (less number of man will take more days to complete the work)
      Total work will be completed by 25 men in = 500/ 25 days = 20 days (increase in the number of men will decrease the number of days needed to complete the work)
    • Therefore, the total work will be completed in 20 days by 25 men.