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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 65687
Q:

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child recieve ?

A) 9 B) 10
C) 11 D) 12
 
Answer & Explanation Answer: A) 9

Explanation:

Let the total number of children be x. 

Then, x * (20% of x) = 405  

=> x * 20x/100 = 405 

15x2 = 405 

 

=> x=45 

 

Number of sweets received by each child = 20% of 45 = 9.

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294 65640
Q:

If 75% of a number is added to 75, then the result is the number itself. The number is :

A) 100 B) 200
C) 300 D) 400
 
Answer & Explanation Answer: C) 300

Explanation:

Let the number be x, Then 

75% of x + 75 = x 

=> x - 75x/100 =75 

=> x =  300 .

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264 64827
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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Q:

Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?

A) 3864 B) 4903
C) 5849 D) 6789
 
Answer & Explanation Answer: A) 3864

Explanation:

Saving  = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400 = Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.

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282 62339
Q:

If A is 40% less than B, then B is how much percentage more than A?

 

 

A) 72.33 B) 60
C) 40 D) 66.66
 
Answer & Explanation Answer: D) 66.66

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Q:

In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent  thus he secured 41% votes of the total voters on the voter list. Percentage votes of the defeated candidate out of the total votes casted is:

A) 47.5% B) 41%
C) 38% D) 45%
 
Answer & Explanation Answer: D) 45%

Explanation:

Let there be x voters and k votes goes to loser then 

 

      0.8x - 120 = k + (k + 200)

 

         k+200 = 0.41x

 

 => k = 1440

 

and  (k + 200) =1640

 

Therefore  1440/3200 x 100 = 45%

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297 59970
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

 

Students who like only Maths forms what percentage of the total number of students in the class?

 

A) 26.67% B) 24.22%
C) 28.80% D) 32.82%
 
Answer & Explanation Answer: A) 26.67%

Explanation:
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