IMPORTANT FACTS AND FORMULAE
1. Concept of Percentage : By a certain percent ,we mean that many hundredths. Thus the x percent means x hundredths and can be 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 particular 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 particular 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 city 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 particular machine be P. Let it depreciates at the rate 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.
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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In Aptitude, Concepts, Formulae, Percentage
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