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:

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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94 27550
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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68 27533
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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54 25704
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 25292
Q:

A bag contains 600 coins of 25 p denomination and 1200 coins of 50 p denomination. If 12% of 25 p coins and 24% of 50 p coins are removed, the percentage of money removed from the bag is nearly :

A) 21.6 % B) 15.3 %
C) 14.6 % D) 12.5 %
 
Answer & Explanation Answer: A) 21.6 %

Explanation:

Total money = Rs.[600*(25/100)+1200*(50/100)]= Rs. 750.

 

25 paise coins removed = Rs. (600*12/100) = 72.

 

50 paise coins removed = Rs. (1200*24/100)= 288.

 

Money removed =Rs.(72*25/100+288*50/100)  = Rs.162.

 

Required percentage = (162/750*100)% = 21.6 %.

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55 23792
Q:

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

56% of 870 + 82% of 180 = 32% of 90 + ?

A) 777 B) 666
C) 606 D) 789
 
Answer & Explanation Answer: C) 606

Explanation:

56% of 870 = 56x870/100 = 487.20

82% of 180 = 82x180/100 = 147.60

32% of 90 = 32x90/100

487.20 + 147.6 - 28.8  =  ?

? = 634.8  - 28.8

? = 606.

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8 22809
Q:

The sum of the number of boys and girls in a school is 150. if the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is : 

A) 60 B) 70
C) 80 D) 90
 
Answer & Explanation Answer: A) 60

Explanation:

We have : x + (x% of 150 )= 150 

=> x+(x/100)*150] = 150

=> 52x = 150  

=> x = (150*2)/5 = 60

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43 22786
Q:

The diference of two numbers is 20% of the larger number, if the smaller number is 20, then the larger number is :

A) 15 B) 25
C) 35 D) 45
 
Answer & Explanation Answer: B) 25

Explanation:

Let the large number be x.

Then x - 20 = 20x/100

=> x - x/5 = 20  => x = 25.

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51 22315