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:

A student has to secure 35% marks to pass in a subject. If he gets 82 and fails by 23 marks. What is the maximum marks of the subject?

A) 300 B) 250
C) 350 D) 400
 
Answer & Explanation Answer: A) 300

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Q:

Marked price of an item is Rs 900. On purchase of 2 items discount is 6%, on purchase of 3 items discount is 12%. Rajani buys 5 items, what is the effective discount?

A) 17.5 percent B) 9.6 percent
C) 35 percent D) 37 percent
 
Answer & Explanation Answer: B) 9.6 percent

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Q:

A student has to secure 40% marks to pass. He gets 67 and fails by 13 marks. What is the maximum marks?

A) 300 B) 200
C) 150 D) 240
 
Answer & Explanation Answer: B) 200

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Q:

Two numbers are 50% and 80% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?

A) 150 percent B) 60 percent
C) 30 percent D) 37.5 percent
 
Answer & Explanation Answer: A) 150 percent

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Q:

If the shopkeeper sells an item at Rs 960 which is marked as Rs 1200, then what is the discount he is offering?

A) 25 percent B) 12 percent
C) 20 percent D) 28 percent
 
Answer & Explanation Answer: C) 20 percent

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Q:

Selling price of a table is Rs 2808. If profit percentage is 17%, then what is the cost price (in Rs) of table?

A) 2288 B) 2300
C) 2400 D) 3285
 
Answer & Explanation Answer: C) 2400

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Q:

The price of rice has increased by 60%. In order to restore the original price, the new price must be reduced by

A) 33 1/3% B) 37 1/2%
C) 40% D) 45%
 
Answer & Explanation Answer: B) 37 1/2%

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Q:

If one-third of a number is 45, then what will be the 45% of that number?

A) 60.75 B) 58.25
C) 61.25 D) 70.75
 
Answer & Explanation Answer: A) 60.75

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