Arithmetic Aptitude :: Percentage
Percentage - Important Formulas
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Concept of Percentage:
By a certain percent, we mean that many hundredths.
Thus, x percent means x hundredths, written as x%.
To express x% as a fraction: We have, x% = \( \frac { X } { 100} \) . Thus, 20% = \( \frac { 20 } { 100} \)= \( \frac { 1 } { 5 } \) . To express as a percent: We have, \( \frac { a } { b } \) = 
\( \frac { a } { b } \) x 100 
%.\( \frac { a } { b } \) Thus, = \( \frac { 1 } { 4 } \) 100 %= 25%. \( \frac { 1 } { 4 } \) -
Percentage Increase/Decrease:
If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
\( \frac { R } { (R*100) } \)x 100 
%If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
x 100 %\( \frac { R } { (R-100) } \) -
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 + \( \frac { R } { 100 } \) n 2. Population n years ago = 1 + \( \frac { R } { 100 } \) n -
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- \( \frac { R } { 100 } \) n 2. Value of the machine n years ago = 1- \( \frac { R } { 100 } \) n 3. If A is R% more than B, then B is less than A by \( \frac { R } { 100+R} \)x 100 %.4. If A is R% less than B, then B is more than A by \( \frac { R } { 100-R} \)x 100 %.