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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:

Read the data given below and answer the questions based on it.

 

In the CBSE Board exams last year, 53% passed in Biology, 61% percent passed in English, 60% in Social studies, 24% in Biology and English, 35% in English and social studies, 27% in Biology and social studies and 5% in none.

 

What is the ratio of percentage of students who passed in Biology and Social Studies but not English in relation to the percentage of students who passed in Social Studies and English but not Biology?

A) 5:7 B) 7:5
C) 4:5 D) 5:4
 
Answer & Explanation Answer: A) 5:7

Explanation:
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2 45273
Q:

30% of a number is 33. What is the number?

 

A) 120 B) 115
C) 105 D) 110
 
Answer & Explanation Answer: D) 110

Explanation:
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3 42428
Q:

Read the data given and answer the following questions

 

In a class of 60 students:

 

42 like Maths,

32 like English,

12 like neither Maths nor English

 

How many students like exactly one subject?

A) 16 B) 12
C) 6 D) 22
 
Answer & Explanation Answer: D) 22

Explanation:
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0 41015
Q:

Ram sell his goods 25% cheaper than Shyam and 25% dearer than Bram. How much % is Bram's good cheaper than Shyam ?

A) 60% B) 40%
C) 50% D) 30%
 
Answer & Explanation Answer: B) 40%

Explanation:

Lets say shyam sells at 100,

 

Since Ram sells 25% cheaper than Shyam,

 

Therefor Ram sells at less than 25% of100 or 75 rs.

 

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

 

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

 

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

 

Hence Brams Good is 40% cheaper than that of Shyam's good.

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77 40160
Q:

The ratio 5 : 4 expressed as a percent equals :

A) 12.5 % B) 40 %
C) 80 % D) 125 %
 
Answer & Explanation Answer: D) 125 %

Explanation:

5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

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154 39337
Q:

270 candidates appeared for an examination, of which 252 passed. The pass percentage is :

A) (91 + 1/3)% B) (93 + 1/3 )%
C) (97 + 1/3 )% D) (98 + 1/3) %
 
Answer & Explanation Answer: B) (93 + 1/3 )%

Explanation:

Pass percentage  =[(252/270)*100] % =280/3 % =9313 9 %

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109 39279
Q:

1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is :

A) 58 B) 62 *2/3
C) 64 D) 67
 
Answer & Explanation Answer: B) 62 *2/3

Explanation:

Total number of students = 1100 + 700 = 1800.

Number of students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.

Number of failues = 1800-672 = 1128.

Percentage failure = (1128/1800 * 100 )% = 62 * 2/3 %. 

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102 36223
Q:

If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by

A) 15 B) 20
C) 25 D) 30
 
Answer & Explanation Answer: B) 20

Explanation:

Let original consumption = 100 kg and new consumption = x kg, 

So, 100 * 6 = x * 7.50 => x = 80kg 

Reduction in consumption = 20%.

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108 36147