# Percentage

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## Basic formulas on Percentage

 1) x% and x/100 mean one and the same thing. 2) y% of x = x% of y = xy/100. 3) In order to convert a percentage into a fraction we have to divide by 100 i.e. x% = x/100. Example: 25% = 25/100 = 1/4; 45% = 45/100 = 9/20 etc. 4) In order to convert a fraction into a percentage we have to multiply by 100. Example: 1/5 = (100/5)% = 20%; 4/25 = (400/25)% = 16% etc. 5) If the value of a number is first increased by a% and then decreased by a% , then the net effect is a decrease of (a2/100)%. Example: Salary of a worker is first increased by 10% and then decreased by 10%. What is the percent change in his salary. Decrease percentage = (102/100)% = 1% decrease 6) When the value of an object is first changed (increased or decreased) by a% and then changed (increased or decreased) by b%, then the net effect is (a + b + ab/100)% NOTE: Increase is represented by a positive sign, decrease is represented by a negative sign. Net effect of a increase or a decrease is according to the sign (positive/negative). Example: The price of an article is first increased by 20% and later on the price is decreased by 25%. Find the net percentage change in final price of the article. Net change = 20 + (-25) + 20(-25)/100 = -10% negative sign indicates reduction in price. 7) If price of a commodity increases by p%, then in order to maintain the same expenditure reduction in consumption is given by 8) If price of a commodity reduces by p%, then in order to maintain the same expenditure increase in consumption is given by 9) If A is p% more than B, then B is less than A by 10) If A is p% less than B, then B is more than A by 11) If 'P' is the present population of a town and is increasing at the rate of r% per annum, then population of the town after N years is 12) If 'P' is the present population of a town and is decreasing at the rate of r% per annum, then population of the town after N years is 13) Increase N by S % = N(1 + S/100) 14) Decrease N by S % = N(1 – S/100) When any number increases by 10%, it becomes 1.1 times of itself. (100% + 10% = 110% = 1.1 times) When any number increases by 20%, it becomes 1.2 times of itself. (100% + 20% = 120% = 1.2 times) When any number increases by 30%, it becomes 1.3 times of itself. (100% + 30% = 130% = 1.3 times) When any number increases by 40%, it becomes 1.4 times of itself. (100% + 40% = 140% = 1.4 times) When any number increases by 5%, it becomes 1.05 times of itself. (100% + 5% = 105% = 1.05 times) When any number decreases by 10%, it becomes 0.9 times of itself. (100% - 10% = 90% = 0.9 times) When any number decreases by 20%, it becomes 0.8 times of itself. (100% - 20% = 80% = 0.8 times) When any number decreases by 30%, it becomes 0.7 times of itself. (100% - 30% = 70% = 0.7 times) When any number decreases by 40%, it becomes 0.6 times of itself. (100% - 40% = 60% = 0.6 times) When any number decreases by 5%, it becomes 0.95 times of itself. (100% - 5% = 95% = 0.95 times)