# 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:

Of the 1000 inhabitants of a town, 60 % are males of whom 120 % are literate. If, of all the inhabitants,  25% are literate, then what percent of the females of the town are literate ?

 A) 32.5 % B) 43 % C) 46.6 % D) 53.2 %

Explanation:

Number of males = 60% of 1000 = 600. Number of females = (1000 - 600) = 400.

Number of literates = 25% of 1000 = 250.

Number of literate males = 20% of 600 = 120.

Number of literate females = (250 - 120) = 130.

Required pecentage = (130/400 * 100 ) % = 32.5 %.

78 35320
Q:

A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast ?

 A) 7500 B) 6200 C) 5600 D) 4700

Explanation:

Let the candidates be A & B
35%-----------A
65%-----------B

Difference of votes (65-35)% = 30%

=>          30% ------- 2250
Then for 100% -------- ?     => 7500

43 34734
Q:

If x is 80% of y, then what percent of 2x is y?

 A) 65.5 % B) 64.5 % C) 63.5 % D) 62.5 %

Explanation:

x = 80 % of y

=> x =(80/100 )y

=> y/x = 5/4

Required percentage =  [(y/2x)*100] % = (5/8*100) % =62.5%

110 34697
Q:

The population of a town was 1,60,000 three years ago, If it increased by 3%, 2.5% and 5% respectively in the last three years, then the present population in

 A) 155679 B) 167890 C) 179890 D) 177366

Explanation:

Present population =  160000 *  (1 + 3/100)(1 + 5/200)(1 + 5/100)= 177366.

84 33580
Q:

Entry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is :

 A) 20 % B) 40 % C) 60 % D) 80 %

Explanation:

Let the total original sale be Rs. 100. Then, original number of visitors = 100.

New number of visitors  =  120/0.75 = 160.

Increase % = 60 %.

105 32459
Q:

In a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?

 A) 324138 B) 349680 C) 509940 D) None of these

Explanation:

Total Population = 728400

Migrants = 35 % of 728400  =  254940

$\inline \therefore$local population = (728400 - 254940) = 473460.

Rural migrants = 20% of 254940 = 50988

Urban migrants = (254940 - 50988) = 203952

Female population = 48% of 473460 + 30% of 50988 + 40% of 203952 = 324138

57 31485
Q:

What percent decrease in salaries would exactly cancel out the 20 percent increase ?

 A) (16 + 2/3) % B) (15 + 2/3)% C) (14 +1/3)% D) (13 + 4/5)%

Explanation:

Let the orginal salary = Rs. 100. New's salary = Rs.120.

Decrease on 120 = 20. Decrease on 100 = [(20/120)*100]% = (16 + 2/3) %.

67 28778
Q:

If the single discount equivalent to successive discounts of 20% and x% is 24%, then the value of x is:

 A) 6% B) 5% C) 4% D) 8%