# Number System - Percentages

## Percentage

Percent means many hundredths.Example: z% is z percent which means z hundredths. It will be written as:

z% = z100

pq as percent: (pq x 100)%

## Commodity

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

[R(100 + R)x 100]%

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

[R(100 - R)x 100]%

## Population

The population of a city is P and let it increases at the rate of R% per annum:

Population after t years: P(1 + R100)t

Population t years ago: P(1 + R100)t

## Depreciation

Let V be the present value of machine. Suppose it depreciates at the rate of R% per annum:

Machine's value after t years:P(1 - R100)t

Machine's value t years ago: P(1 - R100)t

• If P is R% more than Q, then Q is less than P by how many percent?

[R(100 + R)x 100]%
• If P is R% more than Q, then Q is more than P by how many percent?

[R(100 - R)x 100]%

## Solved Examples

Solved Examples

aptitude_percentages.htm