**In this article, we deal with topic of Product Constancy Ratio. This is essentially an application of percentages and can be quite useful while solving problems.**

**What is the Product Constancy Ratio?**

In this concept, we essentially refer to the practice wherein two or more quantities make up a third quantity. With the variation in the numbers of one quantity, the other quantities need to undergo change in order to maintain the same product.

**Let’s take an example.**

Let there be two quantities A and B that multiply to form a quantity P. We can say:

A × B = P

Now if A is increased by a certain percentage, then B is required to be decreased by a certain percentage to keep the product P stable.

The following table illustrates the varying values of A and B that will maintain the same product P.

**Application of Product Constancy: Expenditure Questions**

If the price of a commodity increases or decreases by a%, then, the percentage decrease or increase in consumption, so as not to increase or decrease the expenditure is equal to:

(a/100__+__a) x 100%

**Example:** Length of a rectangle is increased by 33.33%. By what percentage should the breadth be decreased so that area remains constant?

**Solution:** Using the table above:

Since length is increased by 33.33%, the breadth will decrease by 25% to keep area constant.

Let’s make these calculations also.

Let original length= L

Original Breadth= B

Increase length= 4/3 L

Since the area remains same, we can say

L x B = Increased Breadth x 4/3L

Therefore,

Increased breadth = ¾ Original Breadth = 25% reduction in breadth.

**Example:** When speed of a car is increased by 25%, time taken reduces by 40 minutes in covering a certain distance.What is the actual time taken to cover the same distance by actual speed?

**Solution:** We have Speed × Time = Distance

Since speed has been increased by 25%, time will reduce by 20%.

Now, 20% of actual time = 40 min

Actual time = 200 min

**Example:** Price of a commodity has increased by 60%. By what percent must a consumer reduce the consumption of the commodity so as not to increase the expenditure ?

(a) 37%

(b) 37.5%

(c) 40.5%

(d) 60%

### Percentages: The Complete Lesson

#### Table of Contents

**Concept Articles**

**Exercises**

**Tests**