ThePrismSolutions
IMPORTANT FACTS AND FORMULAE
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, ΒΌ =[(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
as not 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/(100R)×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 nyears = 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/(100R))×100]%.

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