## Arithmatical - Percentage

Important facts and formulae
1. Concept of Percentage : By a certain percent, we mean that many hundredths. Thus, x percent means x hundredths, written as x%.I. To express x% as a fraction: We have, x% = x / 100.Thus, 48% = 48 / 100 = 12 / 25.II. To express a / b as a percent : We have a / b = (a / b × 100)%.
2. 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) ×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) ×100]%.

3. Results on Population : Let the population of a town be P now and suppose it increases at the rate of R% per annum, then : 1. Population after n years = P(1 + R / 100 )n.2. Population n years ago = P / (1 + R / 100)n.
4. Results on Depreciation : Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then : 1. Value of the machine after n years = P(1 - R / 100)n. 2. Value of the machine n years ago = P / (1 - R / 100)n.