Percentage
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- Find Percentage: if A is R% more than B, then B is less than A by : $$\frac{R}{(100 + R)}×100\%$$
- Find Percentage: if A is R% less than B, then B is more than A by : $$\frac{R}{(100 − R)}×100\%$$
- Find Percentage Changes: if the price of commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: $$\frac{R}{(100 + R)} ×100\%$$
- Find Percentage Changes: if the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is: $$\frac{R}{(100 − R)} ×100\%$$
- Percentage on Population: Let the population of a town be P now and if it increases at the rate of R% per annum, then:
Population after n years = $$P×\left(1+\frac{R}{100}\right)^n$$
Population n years ago = $$\frac{P}{\left(1+\frac{R}{100}\right)^n}$$
- Percentage on Depreciation: Let the present value of a machine be P. if it depreciates at the rate of R% per annum. then:
Value of the machine after n years = $$P×\left(1−\frac{R}{100}\right)^n$$
Value of the machine n years ago = $$\frac{P}{\left(1−\frac{R}{100}\right)^n}$$
1 The monthly income of a person is ₹ 5000. If his income is increased by 20%, then what will be his new monthly income?
3 A number is increased by 20% and then also increased by 20% again. To get back to the original number, how much should the increased number be reduced by?
4 A student scored 32% marks in science subjects out of 300. How much should he score in language papers out of 200 to get overall 46% marks ?
5 A man loses 12$$\frac{1}{2}$$% of his money and after spending 70% of the remainder, he is left with ₹ 210. Find the amount of money initialy he had:
6 In an office there are 40% female employees. Out of them 40% of females and 60% of males voted for me. What was the percentage of my votes?
7 The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of girls are scholarship recipients, the percentage of students who do not receive a scholarship is:
8 Each student in a class of 60 received sweets equal to 15% of the total number of students. What was the total number of sweets?
