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:

In a test, minimum passing percentage for girls and boys is 35% and 40% respectively. A boy scored 483 marks and failed by 117 marks. What is the minimum passing marks for girls ?

A) 625 B) 525
C) 425 D) 325
 
Answer & Explanation Answer: B) 525

Explanation:

Given 40% minimum passing marks for boys = 483 + 117 = 600
=> 1% = 600/40
=> 100% = 600 x 100/40 = 1500
Minimum passing marks for girls = 35% of 1500 = 35 x 1500/100 = 525.

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Q:

If A is 40% less than B, then B is how much percentage more than A?

 

 

A) 72.33 B) 60
C) 40 D) 66.66
 
Answer & Explanation Answer: D) 66.66

Explanation:
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Q:

What is the value of 88% of 1125 + 20% of 425?

 

A) 1025 B) 1125.2
C) 1075 D) 1055
 
Answer & Explanation Answer: C) 1075

Explanation:
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Q:

While purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?

A) 8 + 15/17 B) 2 + 13/17
C) 3 + 2/17 D) 5 + 13/12
 
Answer & Explanation Answer: A) 8 + 15/17

Explanation:

Total sales tax paid = 7% of Rs, 400 + 9% of Rs. 6400

                            =Rs. (7/100)*400 + (9/100)*6400 = Rs. (28 + 576) = Rs. 604. 

 

Total cost of the items = Rs. (400 + 6400) = Rs. 6800.

 

Required percentage =(604/6800*100) % = 81517%.

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29 16716
Q:

The CO2 emissions in million metric tons over 3 years are given in the following table.

 

What is the increase in the percentage of CO2 emission from year 2016 to 2017?

A) 36.36% B) 26.36%
C) 63.63% D) 36.45%
 
Answer & Explanation Answer: A) 36.36%

Explanation:
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Q:

Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ?

A) 10.769 % B) 11.23 %
C) 10.4 % D) 9.87 %
 
Answer & Explanation Answer: A) 10.769 %

Explanation:

I      II     III

65   58   100

65 -------- 7
100 ------ ?  => 10.769%

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12 16179
Q:

Fresh grapes contain 60% water, while dry grapes contain 40% water. How many kgs of dry grapes can be obtained by 60 kg of fresh grapes?

A) 25 kgs B) 30 kgs
C) 35 kgs D) 40 kgs
 
Answer & Explanation Answer: D) 40 kgs

Explanation:

The fruit content in both the fresh fruit and dry fruit is the same.

Let 'p' kgs of dry grapes are obtained from the 60 kgs of fresh grapes

 

=> 60 x 40100 = p x 60100=> p = 40 kgs.

 

Therefore, 40 kgs of Dry grapes are obtained from 60 kgs of Fresh grapes.

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Q:

The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s ?

A) 24% B) 23 1/3%
C) 25 1/2% D) 22 8/9 %
 
Answer & Explanation Answer: B) 23 1/3%

Explanation:

y=100 x=130

130---------30
100---------? => 23 1/3%

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