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Percentage

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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%.
2. Express each of the following as a decimal.
0.04%
  Sol. = 0.04/100 = 0.0004%.
3. 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.