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# Aptitude – Problems on Percentages

#### Aptitude – Problems on Percentages

In this unit, You can Completely learn Aptitude – Problems on Percentages.

#### Problems on Percentages Important Formula:

1. Concept of Percentage:By a certain percent, we mean that many hundredths.Thus, x percent means x hundredths, written as x%.
 To express x% as a fraction: We have, x% = x . 100
 Thus, 20% = 20 = 1 . 100 5
 To express a as a percent: We have, a = a x 100 %. b b b
 Thus, 1 = 1 x 100 % = 25%. 4 4
2. Percentage Increase/Decrease:If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: R x 100 % (100 + R)

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is: R x 100 % (100 – R)
3. Results on Population:Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
 1. Population after n years = P 1 + R n 100
2. Population n years ago = P 1 + R n 100
4. Results on Depreciation:Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
 1. Value of the machine after n years = P 1 – R n 100
2. Value of the machine n years ago = P 1 – R n 100
 3. If A is R% more than B, then B is less than A by R x 100 %. (100 + R)
 4. If A is R% less than B, then B is more than A by R x 100 %. (100 – R)

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