**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; 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%.

**2.**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]%.

**3. Results on Population :**Let the population of the town be P now and suppose it increases at the rate of

R% per annum, then :

1.
Population after nyeras = P [1+(R/100)]^n.

2.
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

R% per annum. Then,

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

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

^{n}.**5.**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]%.

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