Quick Review: Percentage

The term percentage means "per 100" or "for every hundred".
We should know the percentage table so that we can convert the percentages into fractions for solving the questions quickly.
Percentage Table
Fraction Decimal Percent
1/2 0.5 50%
1/3 0.333... 33.333...%
2/3 0.666... 66.666...%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
2/5 0.4 40%
3/5 0.6 60%
4/5 0.8 80%
1/6 0.1666... 16.666...%
5/6 0.8333... 83.333...%
1/8 0.125 12.5%
3/8 0.375 37.5%
5/8 0.625 62.5%
7/8 0.875 87.5%
1/9 0.111... 11.111...%
2/9 0.222... 22.222...%
4/9 0.444... 44.444...%
5/9 0.555... 55.555...%
7/9 0.777... 77.777...%
8/9 0.888... 88.888...%
1/10 0.1 10%
1/12 0.08333... 8.333...%
1/16 0.0625 6.25%
1/32 0.03125 3.125%
Important Points
  • If A is x% more than that of B, then B is less than that of A by [x/(100+x)* 100]%
  • If A is x% less than that of B, then B is more than that of A by [x/(100-x)* 100]%
  • If A is x% of C and B is y% of C, then: A = (x/y) * 100% of B
  • If two numbers are respectively x% and y% more than the third number, then the first number is [(100+x)/(100+y)* 100]% of the second and the second is [(100+y)/(100+x)* 100]% of the first.
  • If two numbers are respectively x% and y% less than the third number, then the first number is [(100-x)/(100-y)* 100]% of the second and the second is [(100-y)/(100-x)* 100]% of the first.
  • If the price of the commodity increases by x%, then the reduction in the consumption so as not to increase the expenditure is [x/(100+x)* 100]%
  • If the price of the commodity decreases by x%, then the reduction in the consumption so as not to decrease the expenditure is [x/(100-x)* 100]%
  • If two parameters A and B are multiplied to get a product and if P is changed (increased/decreased) by x% and another parameter Q is changed (increased/decreased) by y%, then the net % change in the product (P * Q) is given by [x+y+xy/100]% which represents increase or decrease in the value according as the sign in +ve or –ve. If x or y indicates decrease in percentage, then put –ve sign before x and y, otherwise +ve sign.
  • If the present population of a town (or value of an item) be A and the population (or value of an item) changes at r% per annum, then:
  • Population (or value of the item) after n years = A (1+(r/100))n
  • Population (or value of the item) n years ago = A/(1+(r/100))n
  • In an examination x% and y% students respectively fail in two different subjects while z% students fail in both the subjects, then the percentage of students who pass in both the subjects will be [100–(x+y–z)]%.