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 Percentage Questions

Popular Latest Rated Important Formulae

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, ab=ab×100% .

 

Thus, 14=14×100%=25%

   

 

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is R100+R×100%

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is R100-R×100%

 

 

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 = P1+R100n

 

2. Population n years ago =  P1+R100n

 

 

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 = P1-R100n

 

2. Value of the machine n years ago = P1-R100n

 

 

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

R100+R×100%    

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

R100-R×100%  

Q:

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction ?

A) 31/25 B) 15/17
C) 14/25 D) 11/16
 
Answer & Explanation Answer: B) 15/17

Explanation:

The original fraction is  2551 × 350+100150+100  = 15/17.

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61 31431
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
 
Answer & Explanation Answer: D) 177366

Explanation:

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

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77 30094
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 %
 
Answer & Explanation Answer: A) 32.5 %

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 %.

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70 29614
Q:

If one needs to score 34% to pass a test, the pass marks out of 40 would be:

 

A) 13.2 B) 14.2
C) 13.6 D) 14.6
 
Answer & Explanation Answer: C) 13.6

Explanation:
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10 28738
Q:

What should come in place of question mark (?) in the following question?

45% of 400+ √? = 56% of 750 - 40% of 350

A) 10000 B) 1000
C) 10201 D) 9801
 
Answer & Explanation Answer: A) 10000

Explanation:

45/100×400+√?=56/100 ×750 -40/100 ×350

180 + √? = 420 - 140 180 + √? = 280 √? = 280 - 180 √? = 100 ? = 1002 ? = 10000

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0 28355
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 %
 
Answer & Explanation Answer: C) 60 %

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 %.

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95 28157
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)%
 
Answer & Explanation Answer: A) (16 + 2/3) %

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) %. 

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55 26655
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
 
Answer & Explanation Answer: A) 324138

Explanation:

Total Population = 728400

 

Migrants = 35 % of 728400  =  254940

 

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                        

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44 26545