To express x% as a fraction: We have, x% = x/100
Thus, 20% = 20/100 = 1/5
To express a/b as a percent: We have, a/b = a/b x 100 %.
Thus, 1/4 =(1/4) * 100 % = 25%
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:
R/(100 + R) x 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) x 100 %
Examples:
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
Population after n years = P * [1 +(R/100)]^n
Population n years ago = 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:
Value of the machine after n years = P * [1 -(R/100)]^n
Value of the machine n years ago = P / [1 -(R/100)]^n
If A is R% more than B, then B is less than A by R/(100 + R) x 100 %
If A is R% less than B, then B is more than A by R/(100 - R) x 100 %
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