# Percentage- Facts and Formula

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- 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; 48% =48/100 =12/25, etc.

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

Thus, ¼ =[(1/4)*100] = 25%; 0.6 =6/10 =3/5 =[(3/5)*100]% =60%.

- If the price of a commodity increases by R%, then the reduction in consumption so asnot to increase the expenditure is [R/(100+R))*100]%. If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is [(R/(100-R)*100]%.
- Results on Population : Let the population of the town be P now and suppose it
increases at the rate of R% per annum, then :
- Population after nyeras = 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 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))*100]%.

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

[(R/(100-R))*100]%.