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Percentage

Aptitude

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

10. What is 15 percent of Rs. 34 ?
 
  • A. Rs. 3.40
  • B. Rs. 3.75
  • C. Rs. 4.50
  • D. Rs. 5.10
Ans: D.
Sol.
15% of Rs. 34
= Rs. (15 / 100 x 34)
= Rs. 5.10
 
11. If the price of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
 
  • A. 15%
  • B. 20%
  • C. 25%
  • D. 30%
Ans: B.
Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 6 = x × 7.50 = x = 80 kg.
∴ Reduction in consumption = 20%.
 
 
12. In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subject was
 
  • A. 44
  • B. 45
  • C. 50
  • D. 56
Ans: A.
Sol.
n(A) = 34, n(B) = 42, n(A ∏ B) = 20.
So, n( A ∏ B ) = n(A) + n(B) - n(A ∏ B) = 34 + 42 - 20 = 56.
∴ Percentage failed in either or both the subjects = 56.
Hence, percentage passed = (100 - 56)% = 44%.