Quick Review: Percentage

Percentage Table

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]%
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• 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)]%.