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% = ^{x}/_{100}
Thus, 20% = ^{20}/_{100} = ^{1}/_{5} ;
and 48% = ^{48}/_{100} = ^{12}/_{25}, etc. To express ^{a}/_{b} as a percent : We have, ^{a}/_{b}
= ^{a}/_{b} X 100 %
Thus ^{1}/_{4} = ^{1}/_{4} X 100 % = 25%;
and 0.6 = ^{6}/_{10} = ^{3}/_{5}
= ^{3}/_{5} X 100 % = 60%
If the price of a commodity increases by R%, then the reduction in consumption so
as not to increase the expenditure is _{ }^{ R }_{X 100} % ^{100 + R}
If the price of a commodity decreases by R%, then the increase in consumption so
as not to decrease the expenditure is _{ }^{ R }_{X 100} % ^{100 - R}
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 } ^{P (
1 + 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 - ^{R}/_{}100
)^{n}
2. Value of the machine n years ago = _{= }^{ P } ^{P (
1 - R/100
)
n}
If A is R% more than B, then B is less than A by _{ }^{ R }_{X 100} % ^{100 + R}
If A is R% less than B, then B is more than A by _{ }^{ R }_{X 100} % ^{100 - R}