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