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# Quantitative Aptitude :: Percentage

Home > Quantitative Aptitude > Percentage > Important Formulas

## Percentage Important Formulas

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 $$\frac{a}{b}$$ as a percent: We have, $$\frac{a}{b}$$ = $$\frac{a}{b} \times 100$$%.

Thus, $$\frac{1}{4}$$ = $$\left(\frac{1}{4} \times 100 \right)$$% = 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: $$\left[\frac{R}{(100+R)} \times 100\right]$$%

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

$$\left[\frac{R}{(100-R)} ]\times 100\right]$$%

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 = $$P \times \left(1 + \frac{R}{100}\right)^{n}$$

2. Population n years ago = $$\frac{P}{\left(1 + \frac{R}{100}\right)^n}$$

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 = $$P \times \left(1 - \frac{R}{100}\right)^{n}$$

2. Value of the machine n years ago = $$\frac{P}{\left(1 - \frac{R}{100}\right)^n}$$

3. If A is R% more than B, then B is less than A by

$$\left[\frac{R}{(100 + R)} \times 100\right]$$%.

4. If A is R% less than B, then B is more than A by

$$\left[\frac{R}{(100 - R)} \times 100\right]$$%.
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