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, B and C are three students. A got 36% less marks than B and 16% more marks than C. If B got 145 marks, then what are the marks got by C?

A) 120 B) 110
C) 80 D) 75
 
Answer & Explanation Answer: C) 80

Explanation:
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Q:

A student multiplied a number by 4/5 instead of 5/4. What is the percentage error in the calculation?

A) 56.25 percent B) 18 percent
C) 28.13 percent D) 36 percent
 
Answer & Explanation Answer: D) 36 percent

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Q:

21 is 35 of what number?

A) 60 B) 85
C) 300 D) 21
 
Answer & Explanation Answer: A) 60

Explanation:

The given sentence 21 is 35 of what number means that 

21 is 35 % of what number

Let that number be P

=> 35P/100 = 21

35P = 2100

P = 2100/35 = 300/5 = 60

 

Hence, 21 is 35 of 60.

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Q:

20% of 120?

A) 20 B) 24
C) 32 D) 36
 
Answer & Explanation Answer: B) 24

Explanation:

20% of 120

20 x 120/100

= 4 x 6

= 24

 

Hence, 20% of 120 = 24.

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Q:

Two numbers are 30% and 60% 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) 75 percent B) 42.86 percent
C) 30 percent D) 50 percent
 
Answer & Explanation Answer: A) 75 percent

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Q:

Raman spends 80% of his income. If his income is increased by 25% and the expenditure increase by 10%, then what will be the percentage increase in his savings?

A) 17 B) 70
C) 77 D) 85
 
Answer & Explanation Answer: D) 85

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Q:

A man's annual income has increased by Rs 5 lakhs but the tax on income that he has to pay has reduced from 12% to 10%. He now pays Rs 10,000 more income tax. What is his increased income (in Rs lakhs)?

A) 20 B) 25
C) 15 D) 10
 
Answer & Explanation Answer: B) 25

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Q:

If 1 shirt is offered free on purchase of 4 shirts, what is the effective discount (in %) on each shirt?

A) 25 B) 20
C) 16 D) 24
 
Answer & Explanation Answer: B) 20

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