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## Percentage -> IMPORTANT FACTS AND FORMULAE

 Concepts 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. To express a/b as a percent : we have, a/b = (a/b×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 : Population after n years = P[1+R/100]n. Population n years = p / [1+R/100]n.

## Percentage -> SOLVED EXAMPLES

1. Express each of the following as a decimal. 28% Sol. = 28/100 = 0.28%. Express each of the following as a decimal. 0.04% Sol. = 0.04/100 = 0.0004%. Express each of the following as a fraction. 4% Sol. = 4/100 = 1/25.

## Percentage -> EXERCISE

1. The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?

• A. 48 kg
• B. 49 kg
• C. 50 kg
• D. 51 kg
 Ans: C. Sol. Let the original price be Rs. 100 per kg. Money required to buy 49 kg of rice = Rs. (100 x 49) = Rs. 4900. New price = Rs. 98 per kg. ∴ Quantity of rice bought = [4900 / 98] kg = 50 kg.

2. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had

• A. 588 apples
• B. 600 apples
• C. 672 apples
• D. 700 apples
 Ans: D. Sol. Suppose originally he had x apples. Then, (100 - 40)% of x = 420 ⇔ 60 / 100 × x = 420 ⇔ x = [420×100/60] = 700.

3. Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 1500. then his monthly salary is

• A. Rs. 6000
• B. Rs. 7500
• C. Rs. 8000
• D. Rs. 10,000
 Ans: B. Sol. Saving = [100 - (40 + 20 + 10 + 10]% = 20%. Let the monthly salary be Rs. x. Then, 20% of x = 1500 ⇔ 20 / 100x = 1500 ⇔ x = 1500 × 5 = 7500.