Percentages  Aptitude basics, practice questions, answers and explanations 
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Percentages
 

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
To express a/b as a percent, we have, a/b= (a/b)*100%.
Thus, 1/4= (1/4)*100%= 25%.

1. If A is R% more than B, then B is less than A by R/ (100+R)*100
2. If A is R% less than B, then B is more than A by R/(100-R)*100
3. If the price of a commodity increases by R%, then reduction in consumption, not to increase the expenditure is: R/(100+R)*100
4. If the price of a commodity decreases by R%, then the increase in consumption, not to decrease the expenditure is: R/(100-R)*100

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

3. If a number is increased by x% and thereafter reduced by x%, then the number will be reduced by x²/100 percent

4. If a number is reduced by x% and there after increased by x% then the number will be reduced by x²/100 percent

5. If in an examination, in which the minimum pass percentage is x%, a candidate secures y marks and falls by z marks, then the total number of marks in this examination will be 100*(y+z)/x

6. If in an examination x% and y% candidates respectively fail in two different subjects while z% candidates fail in both the subjects, then the percentage of candidates who pass in both the subjects will be [100-(x+y+z)]%

Tips:

1. If an object's price is increased or decreased by x% and the other factor is decreased by y% then the net effect is given by:
Net Effect= [x+y+xy/100]%

2. If the net effect is nil, ie, there is no loss or no gain, then the above formula becomes: y=100x/100+x

3. If the price of an article is successively increased by x%,y% and z% then single equivalent increase in the price will be [x+y+z+{xy+yz+zx}/(100)+xyz/100²]%

4. If after spending p1% first, then p2% from the remaining and so on, B is the balance amount, then the total (original) amount is given by:
Total amount= B*100*100...../ (100-p2).....

Population formula: 1)If the population increases by x% during the first year, by y% during the second year, by z% during the third year, the population after three years will be:
P(1+x/100)(1+y/100)(1+z/100)