# 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:

Population of Patna city is 96,000, the decreasing rate of population is 800 per year. Population of Patliputra is 68,000, the increasing rate of population is 1200 per year. In how many years will the population of both places be equal?

 A) 10 B) 14 C) 18 D) 22

Answer & Explanation Answer: B) 14

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1 765
Q:

If the selling price of 40 articles is equal to the cost price of 50 articles, then the percentage loss or gain is:

 A) 20% loss B) 25% loss C) 20% gain D) 25% gain

Answer & Explanation Answer: D) 25% gain

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4 759
Q:

A small scale business has the following expenses: procurement (25%), employees' salary (25%) and 50% for maintenance.

If the business pays a total salary of Rs. 2,00,000 then what is its maintenance expense?

 A) ₹ 3,00,000 B) ₹ 2,00,000 C) ₹ 2,50,000 D) ₹ 4,00,000

Answer & Explanation Answer: D) ₹ 4,00,000

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1 752
Q:

A student scored 470 marks in 6 subjects. The maximum marks for each subject was 100%.what was his score in percentage terms?

 A) 67.33% B) 69.45% C) 78.33% D) 78.67%

Answer & Explanation Answer: C) 78.33%

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1 742
Q:

If two numbers are 40% and 70% less than the third number respectively, then second number is how much percent less than the first number?

 A) 100 B) 50 C) 42.5 D) 75

Answer & Explanation Answer: B) 50

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1 739
Q:

of a number will be what percentage of that number?

 A) 44.44 B) 33.33 C) 22.22 D) 11.11

Answer & Explanation Answer: A) 44.44

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1 732
Q:

Sonu saves 15% of her income. If her income increases by 20% and she still saves the same amount as before, then what is thepercentage increase in her expenditure? (correct to one decimal place

 A) 23.5 B) 22.8 C) 23.8 D) 242

Answer & Explanation Answer: A) 23.5

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