Comparing Quantities

Percentage practical problems

Introduction to percentage

• The term "percent" means per hundred or for every hundred. This term has been derived from the Latin word per centum.
• The symbol (%) is used for the term percent.

Example:

13 percent is written as 13%, and it means that "13 out of 100".

Important concepts and formula to remember

Basic Concepts:

Fundamental Formulae:

1. Increase/Decrease in quantity:

(I) If quantity increases by R%, then [Where R denotes the rate of change in percentage]

New quantity = Original quantity + Increases in the quantity

= Original quantity + R% of Original quantity

= Original quantity + R100 of Original quantity

= [1+R100] Original quantity

(II) Similarly, if quantity decreases by R%, then New quantity = [100−R100] ×Original quantity

2. Population:

(I) If a population of a city increases by R% per annum, then the population after 'n' years = (1+R100)n of the original population.

Population after 'n' years = (1+R100)n×Original population

(II) Population 'n' years ago = Original population(1+R100)n

3. Rate is more/less than another:

(I) If a number x is R% more than y, then y is less than x by (R100+R×100)%

(II) If a number x is R% less than y, then y is more than x by (R100−R×100)%

4. Prices of a commodity Increase/Decrease by R %:

(I) If the price of a commodity increase by R%, then a reduction in consumption, so as not to increase the expenditure. [xy×100]%

(II) If the price of a commodity decreases by R%, then increases in consumption, so as not to increase the expenditure. [yx×100]%

If a quantity is increased or decreases by x% and another quantity is increased or decreased by y%, the percent % change on the product of both the quantity is given by require % change = R100

Note: For increasing use (+)ve sign and for decreasing use (−)ve sign.

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