# Arithmetic Aptitude :: Percentage

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## Important Formulas

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Concept of Percentage:

Â Â Â Â Â Â Â Â Â Â  By a certain percent, we mean that many hundredths.Thus, X percent means x hundredths, written as X%.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  To express X% as a fraction: We have, X%Â  = X/100.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Thus, 20% = 20/100 = 15.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  To express a/b as a percent: We have, a/b = (a/b * 100)%.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Thus, 1/4 = (1/4 * 100)% = 25%.

Â Percentage Increase/Decrease:

Â Â Â Â Â Â Â Â Â Â  If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  [R/(100+R) * 100]%

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

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  [R/(100-R) * 100]%

Results on Population:

Â Â Â Â Â Â Â Â Â Â  Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  1. Population after n years = P(1 + R/100)^n

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  2. Population n years ago = P/(1 + R/100)^n

Results on Depreciation:

Â Â Â Â Â Â Â Â Â Â  Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  1. Value of the machine after n years = P(1 - R/100)^n

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  2. Value of the machine n years ago = P/(1 - R/100)^n

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  3. If A is R% more than B, then B is less than A by

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  [R/(100 + R) * 100]%.

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  4. If A is R% less than B, then B is more than A by

Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  [R/(100 - R) * 100]%.

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