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:

Jalal, Amit and Feroz enter into partnership. Jalal invests 4 times as much as Amit and Amit invests three-fourth of what Feroz invests. At the end of the financial year, the total profit earned is Rs. 19,000. Find the share for Jalal.

A) Rs. 15000 B) Rs. 12000
C) Rs. 13000 D) Rs. 10000
 
Answer & Explanation Answer: B) Rs. 12000

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2 656
Q:

Two successive discounts of 10% and 25% are given by Raman on a shirt. If the marked price of the shirt is Rs 600, then what is the value (in Rs) of discount?

 

A) 195   B) 185  
C) 155   D) 135
 
Answer & Explanation Answer: A) 195  

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6 690
Q:

Out of two numbers, 65% of the smaller number is equal to 45% of the larger number. If the sum of the numbers is 2574, then what is the value of larger number?.

 

A) 1521   B) 1471  
C) 1641   D) 1419
 
Answer & Explanation Answer: A) 1521  

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3 595
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

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2 2862
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 percentage of students who passed in all subjects?

A) 8 B) 12
C) 7 D) 10
 
Answer & Explanation Answer: C) 7

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3 2081
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.

 

If the number of students in the class is 200, how many passed in only one subject?

A) 48 B) 46
C) More than 50 D) Less than 40
 
Answer & Explanation Answer: B) 46

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3 2092
Q:

Two successive discounts of 10% and 25% are given by Raman on a shirt. If the marked price of the shirt is Rs 600, then what is the value (in Rs) of discount?

 

A) 195   B) 185  
C) 155   D) 135
 
Answer & Explanation Answer: A) 195  

Explanation:
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2 494
Q:

 Out of two numbers, 65% of the smaller number is equal to 45% of the larger number. If the sum of the numbers is 2574, then what is the value of larger number? 

 

A) 1521   B) 1471  
C) 1641 D) 1419
 
Answer & Explanation Answer: A) 1521  

Explanation:
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2 485