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 price of an article is cut by 31%, to restore to its original value, the new price must be increased by

A) 66 percent B) 44.93 percent
C) 39.76 percent D) 82.5 percent
 
Answer & Explanation Answer: B) 44.93 percent

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Q:

Two numbers are 50% and 90% 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) 80 percent B) 40 percent
C) 44.44 percent D) 400 percent
 
Answer & Explanation Answer: D) 400 percent

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Q:

Jalal, Amit and Feroz enter into partnership. Jalal invests 4 times as much as Amit and Amit invests three-fourth of what Feroz invests. At the end of the financial year, the total profit earned is Rs. 19,000. Find the share for Jalal.

A) Rs. 15000 B) Rs. 12000
C) Rs. 13000 D) Rs. 10000
 
Answer & Explanation Answer: B) Rs. 12000

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Q:

Veer spends 15% of his monthly income on the house rent and 60% of the rest on household expenditure. If he saves Rs. 2210, what is his monthly income?

A) Rs. 8000 B) Rs. 7000
C) Rs. 7500 D) Rs. 6500
 
Answer & Explanation Answer: D) Rs. 6500

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Q:

If the selling price of an item is Rs 9750 after getting a discount of 25%, then what was its marked price (in Rs)?

A) 13000 B) 12187
C) 14000 D) 13187
 
Answer & Explanation Answer: A) 13000

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Q:

A businessman imported Laptops, worth Rs 210000, Mobile phones worth Rs 100000 and Television sets worth Rs 150000. He had to pay 10% duty on laptops, 8% on Phones and 5% on Television sets as a special case. How much total duty (in Rupees) he had to pay on all items as per above details?

A) 36500 B) 37000
C) 37250 D) 37500
 
Answer & Explanation Answer: A) 36500

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Q:

In an election between two candidates, the winning candidate got 70% of the valid votes and won by a majority of 9000 votes. If out of total votes polled 90% votes are valid, then what is the total number of votes polled?

 

A) 30000 B)  25000
C) 22500 D) 27000
 
Answer & Explanation Answer: B)  25000

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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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