Percentage

Percentage

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% = 20/100=1/5 .

To express a/b as a percent: We have, a/b=(a/bx 100)%.

    Thus,1/4=(1/4x 100) %= 25%.

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/(100 + R)x 100)%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

(R/(100 - R)x 100)%

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/100)n

2. Population n years ago =P/(1 +R/100)n

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/100)n

2. Value of the machine n years ago =P/(1 -R/100)n
n
3. If A is R% more than B, then B is less than A by(R/(100 + R)*100)%.

4. If A is R% less than B, then B is more than A by(R/(100 - R)x 100)%

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