| I.Concept of percentages:
By a certain percent, we mean that many hundredths.Thus, x percent means x hundredths, written as x% .
To express x% as fraction: we write 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/bX100)%
Thus,
1/4=(1/4X100)%=25%;
0.6=6/10=3/5=(3/5X100)%=60% etc;
II.Results on prices and consumption:
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) X 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) X 100]%
III. Results on population:
Let the population of a town be P now and suppose it increases at the rate of R% per annum , then:
1.Population after n years=P(1+R/100)n
2.Population n years ago=P/(1+R/100)n
IV. Results on Depreciation:
Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
1. Value of the machine after n year =P(1-R/100)n
2. Value of the machine n years ago = P/(1-R/100)n
V.Comparision
If A is R% more than B, then B is less than A by
[R/(100+R)X100]%
If a is R% less than B, then B is more than A by
[R/(100-R)X100]%
Labels: Quantitative aptitude (concepts) |
