### Focus Topic: Percentage (Arithmetic/Commercial Mathematics)

#### Tricks and Application of Percentage: Product Constancy Ratio and Successive Percentage Change

Using the day-1 of this preparation plan, you should have mastered the basic concepts of Percentages. But along with these basic concepts, you also need to work on some advanced level concepts and questions that make a frequent appearance in examinations.

On a number of occasions, in percentages, you find questions where you are given two or more percentage changes and then the net percentage change is asked. If you solve these questions by normal methods you learnt in schools, then the solutions might become lengthy and time-consuming. But this is where we are going to help you out with a little trick that can come in handy for solving percentage based questions. In today’s post, you learn how to solve the questions on percentage change by using a simple concept.

In these questions, generally two things are interrelated. If one thing or variable is changed by certain percentage, then we have to find the percentage effect on the other thing or variable. Broadly, these questions come under the topic head of *Product Constancy Ratio.*

Let’s take up an example to understand how this works.

Example question: **“If the price of rice is increased by 50%, by what percent its consumption should be reduced so that the expenditure does not change”**.

**Solution:**

Let the price of rice be Rs. 10 per kg.

The increased price: Rs. 15 kg.

Let the initial consumption be 10 kgs.

Total expenditure= Rs. 100

This has to remain constant.

Therefore, new consumption= 100/15 = 6.67 Kgs.

This is 33.33% less than the original consumption.

In the above case, we have had to run these calculations to arrive at this answer but what if this was not required of us? You can avoid these simple calculations and improve your speed in this topic by learning more about Product Constancy Ratio. We have a detailed article, accompanied with an exercise, on this topic for you. Go through the link given below and learn more about this trick to solve some percentage based questions quickly.