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:

A man wills 40% of his wealth to his wife and rest to his children. What percent of the wealth willed to the wife do the children get?

A) 150 B) 66.6
C) 50 D) 20
 
Answer & Explanation Answer: A) 150

Explanation:
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Q:

A man’s average monthly expenditure for the first four months of the year was Rs. 231.25. For the next five months, the average monthly expenditure was Rs. 22.75 more than what it was during the first four months. If the person spent Rs. 605 in all during the remaining three months of the year, find what percentage of his annual income of Rs. 3500 did he save in the year?

A) 10% B) 15%
C) 20% D) 25%
 
Answer & Explanation Answer: C) 20%

Explanation:

A man's average monthly expenditure for the first four months of the year = Rs.231.25.
For four month = 231.25 * 4 = Rs. 925
For next five month he spend = 231.25 + 22.75 for one month.
In five month he spend = (231.25 + 22.75) X 5 = 1270
If the person spent Rs. 605 in all during the remaining three months of the year,
Total expense = 925+1270+605= 2800
Saving = 3500-2800 = 700
% saving = 700/3500 * 100 = 20%

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Q:

A person purchase 50 mangoes he sells 10 at 20% profit, 20 at 30% profit and rest got rotten. Find its total loss or profit%?

A) 28% B) 26%
C) 24% D) 22%
 
Answer & Explanation Answer: C) 24%

Explanation:

Let the cost price of each mango be Rs. 1

So 50 mangoes costs = Rs. 50

20% Profit on Selling Price of 10 mangoes = Rs. 12 

30% Profit on Selling Price of 20 mangoes = Rs. 26

Total = Rs. 38

Loss = 50 - 38 = 12

 

Loss% = (12/50) x 100 = 24%.

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5 2954
Q:

If the side of square is increased by 6%, then what will be the percentage increase in its area?

A) 3.2 B) 12.04
C) 12.12 D) 12.36
 
Answer & Explanation Answer: D) 12.36

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2 2934
Q:

Write 0.125 as a percent %?

A) 12% B) 12.5%
C) 13% D) 13.5%
 
Answer & Explanation Answer: B) 12.5%

Explanation:

Here to convert 0.125 into %

First convert to fractio

Multiply and divide by 1000

=> 0.125 x 10001000 = 1251000 = 18

=> Now, in percentage18 x 100 = 12.5%

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7 2900
Q:

A shopkeeper offers the following 3 schemes. Which scheme has the maximum discount percentage?

 

I. Two successive discounts of 30% and 20%

 

II. Buy 4 get 7

 

III. Buy 4 get 3 free

 

A) Only I B) Only III  
C) Only II and III   D) All are equal
 
Answer & Explanation Answer: A) Only I

Explanation:
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1 2858
Q:

A woman suffered 20% loss on first investment and made 10% profit at second investment and 12 ½% profit on the third investment. If the invested amount be in the ratio of 4 : 5 : 3, find her profit percentage?

A) 0.625% B) 1.205%
C) 0.987% D) 0%
 
Answer & Explanation Answer: A) 0.625%

Explanation:

From the given data,

let the amounts invested be 4p, 5p and 3p

Net profit = Total profit - Total loss

= 10x5p/100 + 25x3p/200 - 20x4p/100

= 0.875p - 0.8p

= 0.075p

Therefore, profit% = (Net profit/Total investment) x 100

= 0.075 x 100/12 

= 0.0625%

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9 2730
Q:

1 bottle of honey costs Rs 240 but a pack of 4 of the same bottles costs Rs 768. What is the effective discount (in %) on the pack?

A) 16 B) 25
C) 10 D) 20
 
Answer & Explanation Answer: D) 20

Explanation:
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