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:

Ticket for an adult is Rs 1200 and a child is Rs 800 respectively. One child goes free with two adults. If a group has 25 adults and 5 children what is the discount the group gets?

A) 17.24 percent B) 24. percent
C) 24.41 percent D) 11.76 percent
 
Answer & Explanation Answer: D) 11.76 percent

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Q:

If P = 5X and Q = X, then P is how much percentage more than Q?

A) 80 B) 320
C) 500 D) 400
 
Answer & Explanation Answer: D) 400

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Q:

A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is

A) 4% B) 6%
C) 10% D) 12%
 
Answer & Explanation Answer: C) 10%

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Q:

If 9/4th of 7/2 of a number is 126, then 7/2th of that number is _____.

A) 56 B) 284
C) 72 D) 26
 
Answer & Explanation Answer: A) 56

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Q:

The price of an article is discounted by 25%, to restore to its original value, the new price must be increased by

A) 57 percent B) 36.31 percent
C) 71.25 percent D) 33.33 percent
 
Answer & Explanation Answer: D) 33.33 percent

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Q:

30% discount is offered on an item. By applying a promo code the customer wins 10% cash back. What is the effective discount?

A) 40.7 percent B) 40 percent
C) 37 percent D) 13 percent
 
Answer & Explanation Answer: C) 37 percent

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Q:

The sum of three numbers is 67. If the ratio of the first number to the second number is 3 : 5 and that of the second number to the third number is 4 : 7, then what is the second number ?

A) 20 B) 24
C) 18 D) 16
 
Answer & Explanation Answer: A) 20

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Q:

In a company 2/3 of the workers are girls, 1/2 of the girls are married and 1/3 of the married girls live in hostel. If 3/4 of the boys are married and 2/3 of married boys live in hostel. Calculate the part of workers who don’t live in hostel.

 

A) 11/18 B) 15/18  
C) 17/18   D) 13/18
 
Answer & Explanation Answer: D) 13/18

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