Ratios and Proportions

Unitary Method

In our daily lives when buying items like vegetables, the seller mentions the wholesale prices. For example, suppose we buy 5kg of sugar for 100 Rs. How can we find out the price for a unit kg that is 1 kg of sugar? The answer to this is the unitary method. Further, we can use this to calculate the price of multiple units, given the knowledge of the cost of a single unit. Given its importance in our daily lives, let us understand about the unitary method.

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Unitary Method

Unitary Method

The word unitary refers to a single or an individual unit. Hence this method aims at determining values in relation to a single unit. For example, if a car runs 44 km on 2 litres of petrol then we can use the unitary method to find out the kilometres it will cover on 1 litre of petrol.

In other words, the method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method. Let us understand the application of unitary method by an example:

Suppose Ram buys a dozen(12) bananas for 36 Rs. The cost of 12 bananas = 36 Rs. The cost of 1 banana = 36÷12 = 3 Rs. Hence a single banana costs 3 rupees. Now, suppose we need to find the cost of 15 bananas. This can be done as: the cost of 15 bananas = 3 Rs. × 15 units = 45 Rs.

In essence, if the value of multiple items is given to us, we simply divide the total value by the number of units to obtain the value of one unit. This is the unitary method.

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Solved Examples for You

Question 1: The cost of 10 notebooks is 300 Rs. Find:

  • The number of notebooks that can be purchased with 420 Rs.
  • The cost of 5 notebooks

Answer : It is given that the cost of 10 notebooks = 300 Rs. Hence the cost of 1 notebook = 30 Rs. Now,

  • The number of notebooks that can be purchased with 30 Rs. = 1. The number of notebooks that can be purchased with 1 Re. = 1/30. Hence, the number of notebooks that can be purchased with 420 Rs. = 1/30 ×420= 14 notebooks
  • The cost of 1 notebook = 30 Rs. The cost of 5 notebooks = 30 Rs. × 5 = 150 Rs.

Question 2: If 45 students can consume a stock of food in 22 months, then for how many days the same stock of food will last for 27 students?

  1. 100 days
  2. 144 days
  3. 160 days
  4. 180 days

Answer : The correct answer is “A”. The food will last for 100 days. Let us see how. According to the first condition, students consume food in 2 months, i.e. in 60 days. So this ratio would be 45:60

According to the second condition, the same amount of food is consumed by 27 students in x days. So that ratio would be 27:x. By Inverse Proportion,

45 × 60 = 27 × x

x = (45 × 60) / 27

x = 100

Question 3: What is the formula for the unitary method?

Answer: In case we are having the value of multiple items with us, then we will simply divide the total value with the number of units to get the value of 1 unit and this process is known as the unitary method.

Question 4: What is the unitary method for the percentage?

Answer: We can use the unitary method to find out 100 % of an amount given a percentage of that amount. For instance, if 10 % of an amount of money is Rs.23, then its 100 % is 10 × Rs.23 = Rs.230.

Question 5: What is the unitary ratio?

Answer: When one side of any ratio is one then the ratio is called a unitary ratio. This is useful while comparison.

Question 6: What is the unitary method in mathematics?

Answer: The unitary method is generally a way of finding out thesolution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value. However, this technique is useful for finding out the value of a unit from the value of a multiple, and therefore, the value of a multiple.

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