Percentage

Concept of Percentage

By a certain percent, we mean that many hundredths.
Thus, x percent means x hundredths denoted by x %.

Expressing a percentage as a fraction or decimal number:

i) x % = x/100

ii) 50 % = 50/100 = 1/2 = 0.5

Expressing a fraction or decimal number as percentage:

i) x/y = {(x/y) x 100} %

ii) 1/4 = {(1/4) x 100} % = 25 %

Percentage Increase/Decrease

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

[{R/(100-R)} x 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 + R/100)ⁿ

2. Population n years ago = P/{(1 + R/100)ⁿ}

Results on Depreciation

Let the present value of a machine P. It depreciates at a rate of R% per annum. Then

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

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

3. If A is R% more than B, then B is less than A by [{R/(100+R)} x 100] %

4. If A is R% less than B, then B is more than A by [{R/(100-R)} x 100] %

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