# Important Formulas - Percentage - Tricks & Shortcuts

1) 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

To express a/b as a percent: We have, (a/b)=((a/b)*100)%.

Thus, 1/4 = ((1/4)*100)% = 25%.

2. 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))*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))*100]%

3. Results on Population:

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

i) Population after n years = P(1+(R/100))^n

ii) Population n years ago = (P)/(1+(R/100))^n

4. Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

i) Value of the machine after n years = P(1-(R/100))^n

ii) Value of the machine n years ago = (P)/(1-(R/100))^n

iii) If A is R% more than B, then B is less than A by [((R)/(100+R))*100]%

iv)  If A is R% less than B, then B is more than A by [((R)/(100-R))*100]%