Percentages

Product Constancy

Today, we are going to discuss product constancy. It is one the important topics in percentage section. It is also one of the basic topics you need to prepare for the percentage. In the section below we will solve examples on consumption, and heights. Let us see!

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What is Product Constancy?

Product constancy means the consistency of the product even though there is an increase or decrease in its price. You can also call product constancy as inverse proportionality. In product constancy, you have to reduce the consumption when there is an increase in price so that your budget remains the same.

Product constancy

Suppose you have a situation where the price of a product has risen by 25%. But you need to keep your total expenditure constant. So, what would you do? You will try and manage the only thing that is in your hand i.e. consumption. You can reduce the consumption accordingly so that whatever there is an increase in price, the total expenditure will remain same. Here as mentioned, the price of the product is increased by 25% so what should be the decrease in consumption to meet your expenses?

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Here, in this question suppose that earlier the price of the product was Rs. 100. Now with the increase in price, it becomes Rs. 125. So now for Rs. 100 the 80% of the same product will be available. So, you will get 80% of the product for Rs. 100 wherein earlier you used to get whole 100%. So, this is a difference of 20%. Thus you need to reduce your consumption by 20% so that your total expenditure will remain the same.

Here below is the product constancy table which denotes the increase and decreases in ratio and the percentage so that your total expenditure will be same. You can remember some of the values of this table so that the questions related to product constancy will become easier for you.

Product AB is constant A increases( in %) B decreases (in %)
Value 1 9.09 8.33
Value 2 10 9.09
Value 3 11.11 10
Value 4 12.5 11.11
Value 5 14.28 12.5
Value 6 16.66 14.28
Value 7 20 20
Value 8 25 20
Value 9 33.33 25
Value 10 50 33.33
Value 11 60 37.5
Value 12 66.66 40
Value 13 75 42.85
Value 14 100 50

Examples Based on Consumption

Q. Mr Shah is worried about his yearly budget. The price of wheat has been increased by 40%. So, by what percent should he reduce the consumption of wheat so that he easily balance his yearly budget?

A. 14.28 %                B. 33.33 %
C. 25 %                     D. 28.56 %

Generally, in product constancy, these types of questions are asked and you need to find the reduction in consumption so that the total expenditure remains the same.

To find the total reduction you can use the formula given for the absolute change. Here, suppose the initial prices were Rs. 100. Now, the prices have been increased by 40%, so the new prices will be Rs. 140. So, the reduction in consumption = 40/140 x 100 = 28.56 %. So, the correct answer is D.

Q. In the above question, if Mr Shah wants to increase his budget by 5% on his basic expenditure on wheat than what should be the corresponding decrease in consumption so that the expenditure only exceeds by 5 %?

A. 25 %                  B. 28.56 %
C. 33.33 %            D. 20 %

Here the with the increase in prices the expenditure is increased by 5 %. So, 5 % on 100 will be Rs. 5. So, the new expenditure for Mr Shah will be Rs. 105. Now, you need to find the reduction from the increase in the price of wheat to the new increase in expenditure i.e. 140 to 105. This is a decrease of Rs. 35. Which is 25 % of 140. So, the reduction in consumption will be 25 %, so that the expenditure does not increase by more than 5 %. So, the correct answer is A.

Example Based on Heights

Q. In a physical test, the professor by mistake wrote the height of the student 25% more than his actual height. Further, in the next test, it was realized that his actual height was 5 feet 6 inches. Find the percentage correction made by the committee from the height mentioned in the first test to the height found out in the second test.

A. 25                     B. 16.66
C. 20                     D. 28.56

Here, the professor made an error and increased the height of the student by 25 %. So, to make the correction you need to go back to his original height. Using the product constancy table, you can see that whenever there is an increase in 25% you need to reduce it by 20 %. So that you can go back to the original. Thus the height of the student needs to be reduced by 20 % to get this original height. Thus, the correct answer is C.

Practice Questions

Q. The height of the triangle is increased by 40 %. What can be the maximum percentage increase in the length of the base so that the increase in area is restricted to a maximum of 60 %?

A. 20 %               B. 50 %
C. 14.28 %          D. 25 %

Ans: The correct answer is C.

Q. The price of the sugar reduces by 20 %. How much of sugar can be brought by the money that was sufficient earlier to buy 20 kg of sugar?

A. 15 kg                B. 5 kg
C. 30 kg              D. 25 kg

Ans: The correct answer is D.

Q. A number was divided by 5 instead of it being multiplied by 5 due to a computer glitch. What was the change in the percentage result due to this error?

A. 200 %            B. 2400 %
C. 95 %               D. 96 %

Ans: The correct answer is D.

Q. The price of rice was reduced by 25%, but in spite of the decrease in price, a man ends up increasing his expenditure of rice by 20 %. What was the percentage change in his monthly consumption of rice?

A. +50 %            B. +60 %
C. +33.33 %      D. -10 %

Ans: The correct answer is B.

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