Percentage Change

In this topic, we are going to discuss the concepts of percentage change. We see percentage change in our everyday life. From the increase in price to decrease in price, from more discounts, there is a change in percentage everywhere.

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Percentage Change

The change in the value of product refers to as the amount of percentage change in the product. In percentage whenever the value of measured changes, the change can be captured in two ways. They are:

1. Absolute value change
2. Percentage change
Both these terms have their advantages as well as disadvantages.

1. Absolute Value Change

Absolute value change refers to the actual change in the measured quantity. It means the direct change in the product. For example, if the sales of the product in 1st year is 200 crore and in the second year it 220 crores, then the absolute value of the change will be 100 crores.

2. Percentage Change

This change in percentage can be obtained through the following formula.

Percentage change = Absolute value change/ original quantity x 100

= 20/200 x 100 = 10%

It is important to note here that the percentage change calculations are usually calculated on the original quantity unless it is mentioned in the question.

We will understand the concept of percentage change through some examples.

Example Based on Population

Q. The population of a city grew from 40 lakh to 44 lakh. Find the
a) percentage change
b) percentage change based on the final value of the population.

Here, we are required to find two things. First, we need to find the change in percentage from 40 to 44, then based on the final value we need to find the percentage change.

Change in percentage = absolute value change/ original quantity x 100
The increase in population is 4 lakh and the original population was 40 lakh. So, the change in percentage = 4/40 x 100 = 20%.

Now, we are required to find the change in percentage but the base should be final value.

Change in percentage = 4/44 x 100 = 9.09%.

Example Based on Price Hike

Q. Due to a 25% hike in the price of sugar, a person is able to purchase 20 kg less of sugar for Rs. 500. What was the initial price of sugar?

A. Rs. 4
B. Rs. 5
C. Rs. 6
D. Rs. 7

In this question, one thing you need to remember is that with the increase in price there will be the decrease in consumption. This is how the percentage works. Since the prices are rising by 25%, in this case, the consumption of the sugar will have to be reduced by 20% so that budget remains the same. But here it is given that there is an actual reduction of 20 kg. So, 20% of the decrease in consumption will be equal to 20 kg drop in the consumption.

So, the original consumption was 100 kg of sugar. While the total money spent on sugar was Rs. 500. So, the initial price of the sugar was Rs. 5/kg. So, the correct answer is B.

Through product constancy table, you can easily learn hike and reduction of consumption. We have discussed it in our other article.

Example Based on Area

Q. If the breadth of the rectangle is increased by 20 % and the length of the rectangle is decreased by 10 %, then what is the percent change increase in the area of the rectangle?

A. 6 %         B. 8 %             C. 10 %              D. 12 %

Ans: The area of a rectangle is l x b.

So, due to increase and decrease in breadth and length of the rectangle respectively the new area will, 0.9l x 1.2b = 1.08 lb. Thus the increase in new area is 8 %. So, the correct answer is B.

Practice Questions

Q. The price of the ticket from Delhi to Mumbai increased by 8% and thereby one ends up paying 5940 for the journey. Find the rate of tickets before the increase in prices.

A. Rs. 5500      B. Rs. 5600        C. Rs. 5700       D. Rs. 5800

Ans: The correct answer is A.

Q. The price of the petrol goes down by 10 % and the consumption increases by 20 %. What was the original change in the expenditure on petrol?

A. -8 %          B. +8%           C. -10%            D. +10%

Ans: The correct answer is B.

Q. The number of applicants for the government jobs increased by 75% from 1990 to 1995, From 1995 to 2000 there was an increase of 100 % in the number of applicants. Find the percentage increase in the number of applicants from 1990 to 2000.

A. 200 %      B. 220 %         C. 240 %         D. 250 %

Ans: The correct answer is D.

Q. Raman’s salary was reduced by 30 % and then increased by 30 %. What was the net change in the salary of Raman?

A. -6 %        B. -4 %            C. +6 %           D. No change

Ans: The correct answer is A.

Q. The candidate got 56 % of the votes cast in an election. He won by 144 votes. What was the total number of voters on the voting list if 80 % people cast their vote and there was not a single invalid vote?

A. 360         B. 1500          C. 1800            D. 720

Ans: The correct answer is B.