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:

If 90% of A = 30% of B and B = x% of A, find x.

A) 600 B) 900
C) 300 D) 1200
 
Answer & Explanation Answer: C) 300

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Q:

If a retailer offers a discount of 28% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

A) 18.25 percent B) 22 percent
C) 38.88 percent D) 28 percent
 
Answer & Explanation Answer: C) 38.88 percent

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Q:

Two students appeared for an examination. One of them secured 16 marks more than the other and his marks were 75% of the sum of their marks. The marks obtained by them are

A) 98 and 82 B) 49 and 33
C) 96 and 80 D) 24 and 8
 
Answer & Explanation Answer: D) 24 and 8

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Q:

Ravi had five subjects in his final examination. The maximum marks in each subject are 100. If his percentage in four subjects is 80, and he scores 65 marks in the fifth subject, determine his overall percentage for the five subjects.

A) 0.78 B) 0.79
C) 0.77 D) 0.76
 
Answer & Explanation Answer: C) 0.77

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Q:

Two numbers are 40% and 50% 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) 16.67 percent B) 20 percent
C) 10 percent D) 25 percent
 
Answer & Explanation Answer: B) 20 percent

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Q:

Weight of Ayush and Abhishek are in the ratio of 6:11. Abhishek's weight increases by 25% and total weight of Ayush and Abhishek both increases by 40%. If total weight becomes 119 kg, then wat is the weight (in kg) of Ayush after the increment?

A) 45.5 B) 30
C) 50.25 D) 47.75
 
Answer & Explanation Answer: C) 50.25

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Q:

There are 1400 students in a school, 25% of those wear spectacles and 2/7 of those wearing spectacles are boys. How many girls in the school wear spectacles?

A) 250 B) 100
C) 200 D) 300
 
Answer & Explanation Answer: A) 250

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Q:

In the last financial year, a car company sold 41,800 cars . In this year, the target is to sell 51,300 cars . By what percent must the sale be increased ?

A) 11 9/22% B) 8 9/22%
C) 8 11/23% D) 22 8/11%
 
Answer & Explanation Answer: D) 22 8/11%

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