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:

The weights of two iron balls are 3.5 kg and 7.5 kg. What is the percentage weight of the 1st ball with respect to 2nd ball.

A) 46 2/3% B) 35%
C) 46 1/3% D) 45%
 
Answer & Explanation Answer: A) 46 2/3%

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Q:

If 35% of (x + y) = 40% of (x – y), then x is what percentage of y?

A) 1500 B) 150
C) 15 D) 105
 
Answer & Explanation Answer: A) 1500

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Q:

If the edge of a cube is increased by 10%, then what will be the percentage increase in its volume ?

A) 30 B) 31.3
C) 136.1 D) 33.1
 
Answer & Explanation Answer: D) 33.1

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Q:

Marked price of an item is Rs 500. On purchase of 2 items discount is 8%, on purchase of 3 items discount is 16%. Radha buys 5 items, what is the effective discount?

A) 20.4 percent B) 23.25 percent
C) 12.8 percent D) 35 percent
 
Answer & Explanation Answer: C) 12.8 percent

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Q:

If U = 450 and V = 585, then V is how much percentage more than U?

A) 130 B) 23.07
C) 25 D) 30
 
Answer & Explanation Answer: D) 30

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Q:

An engineering student has to secure 25% marks to pass. He gets 47 and fails by 43 marks. What are the maximum marks of the examination?

A) 385 marks B) 410 marks
C) 360 marks D) 435 marks
 
Answer & Explanation Answer: C) 360 marks

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Q:

If the successive discounts be 20% , 10% and 5% , then the single equivalent rate of discount is

A) 31.6% B) 31.5%
C) 31% D) 31.4%
 
Answer & Explanation Answer: A) 31.6%

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Q:

A total amount of Rs. 1560 is to be divided among A, B, C such that A gets 50% of what B gets and B gets 20% of what C gets. How much will B get ?

A) Rs. 540 B) Rs. 440
C) Rs. 280 D) Rs. 240
 
Answer & Explanation Answer: D) Rs. 240

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