# Percentage Questions

FACTS  AND  FORMULAE  FOR  PERCENTAGE  QUESTIONS

I.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;

48% = 48/100 = 12/25, etc.

To express a/b as a percent : We have, $\frac{a}{b}=\left(\frac{a}{b}×100\right)%$ .

Thus, $\frac{1}{4}=\left(\frac{1}{4}×100\right)%=25%$

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is $\left[\frac{R}{\left(100+R\right)}×100\right]%$

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is $\left[\frac{R}{\left(100-R\right)}×100\right]%$

III. Results on Population : Let the population of the town be P now and suppose it increases at the rate of R% per annum, then :

1. Population after n years = $P{\left(1+\frac{R}{100}\right)}^{n}$

2. Population n years ago =  $\frac{P}{{\left(1+\frac{R}{100}\right)}^{n}}$

IV. Results on Depreciation : Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then,

1. Value of the machine after n years = $P{\left(1-\frac{R}{100}\right)}^{n}$

2. Value of the machine n years ago = $\frac{P}{{\left(1-\frac{R}{100}\right)}^{n}}$

V. If A is R% more than B, then B is less than A by

$\left[\frac{R}{\left(100+R\right)}×100\right]%$

If A is R% less than B , then B is more than A by

$\left[\frac{R}{\left(100-R\right)}×100\right]%$

Q:

If the cost of production doubles in a period of 3 years, then the corresponding maintenance cost in rupees will be

 A) ₹ 75 lakh B) ₹ 12.5 lakh C) ₹ 25 lakh D) ₹ 125 lakh

Answer & Explanation Answer: C) ₹ 25 lakh

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Q:

If the production increases to five times of the present cost, then the percentage increase of the cost is

 A) 50% B) 400% C) 300% D) 500%

Answer & Explanation Answer: B) 400%

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Q:

A number is increased by 30%, then decreased by 30%, then further decreased by 30%. What is the net increase/decrease percent in the number(correct to the nearest integer)?

 A) 36% decrease B) 36% increase C) 40% increase D) 40% decrease

Answer & Explanation Answer: A) 36% decrease

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Q:

A certain amount invested at a certain rate, compounded annually, grows to an amount in two years, which is a factor of 1.1881 more than to what it would have grown in three years. What is the rate percentage?

 A) 8 B) 8.1 C) 9.2 D) 9

Answer & Explanation Answer: D) 9

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