# Quick Review: Percentage

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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)]%.
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