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:

At 13% discount the selling price of a oven is Rs 18000, what is the selling price if the discount is 27.5%?

A) Rs 10875 B) Rs 12288.75
C) Rs 15000 D) Rs 16638.75
 
Answer & Explanation Answer: C) Rs 15000

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Q:

Two numbers are 30% and 37% 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) 10 percent B) 7 percent
C) 11.11 percent D) 18.92 percent
 
Answer & Explanation Answer: C) 11.11 percent

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Q:

A shopkeeper marks up his wares by 60% and offers 25% discount. What will be the selling price (in Rs) if the cost price is Rs 1600?

A) 1920 B) 2000
C) 2120 D) 2200
 
Answer & Explanation Answer: A) 1920

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Q:

Daily local train ticket costs Rs 60 and Monthly Pass costs Rs 1566. If I buy the Monthly Pass and travel for 29 days in a month than I save?

A) 10 percent B) 14 percent
C) 15 percent D) 12 percent
 
Answer & Explanation Answer: A) 10 percent

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Q:

The income of X is 60% more than Y’s income and the income of Y is 40% more than Z’s income. X’s income is how much percentage more than Z’s income?

 

A) 134 B) 224
C) 100 D) 124
 
Answer & Explanation Answer: D) 124

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Q:

Which single discount will be equal to two successive discounts of 12% and 5%?

A) 17% B) 8.5%
C) 16.4% D) 15.2%
 
Answer & Explanation Answer: C) 16.4%

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Q:

The price of an article is cut by 42%, to restore to its original value, the new price must he increased by ______.

A) 42 percent B) 72.41 percent
C) 29.58 percent D) 52.5 percent
 
Answer & Explanation Answer: B) 72.41 percent

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Q:

What will be the net discount (in percentage) for two successive discounts of 30% and 20%?

A) 50 B) 56
C) 44 D) 54
 
Answer & Explanation Answer: C) 44

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