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:

100 percent of which number is 20?

A) 100 B) 500
C) 20 D) 0
 
Answer & Explanation Answer: C) 20

Explanation:

Let the rquired number be 'P'

According to the question,

100 x P100 = 20=> P = 20 x 100100 = 20

Hence, 100 percent of the number 20 is 20.

 

Now, you can also try for

20 percent of what number is 100

20 x P100 = 100=> P = 100 x 10020 = 500=> P = 500

Hence, 20 percent of the number 500 is 100.

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13 5846
Q:

63.5% of 8924.2 +? % of 5324.4 = 6827.5862

A) 28 B) 22
C) 18 D) 12
 
Answer & Explanation Answer: B) 22

Explanation:

63.5% of 8924.2 +? % of 5324.4 = 6827.5862

=> 63.5% of 8925 + ? % of 5325 = 6830

=> 6830 ~= 5320 + ?(5325)/100

=> ? ~= 22

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6 5730
Q:

In a hoel, 60% had vegetarian lunch while 30% had non-vegetaian lunch and 15% had both types of lunch. If 96 people were present, how many did not eat either type of lunch ?

A) 24 B) 30
C) 36 D) 42
 
Answer & Explanation Answer: A) 24

Explanation:

n (A) = (60/100 * 96) = 288/5, n (B) = (30/100 * 96) = 144/5, n (A ∩ B) = (15/100 * 96) = 72/5.

n(A ∪ B) = n (A) + n (B) - n (A ∩ B) = 72.

So, people who had either or both types of lunch = 72.

Hence, people who had neither type of lunch = (96 - 72)= 24.

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1 5681
Q:

What is 85 of 352?

A) 21.5% B) 24.14%
C) 23.68% D) 25.47%
 
Answer & Explanation Answer: B) 24.14%

Explanation:

Here 85 of 352 => 85 is what percent in 352

Let p% of 352 is 85

Percentage(%) is generally calculated in the total of 100.

=> p x 352/100  = 85

=> p = 8500/352  = 24.14%

 

Hence, 85 is 24.14% of 352.

 

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4 5669
Q:

Value of vehicle at end of each year depreciates at the rate of 3/5th of value at the beginning. If Initial value is 10,000Rs then at the end of three years its value is ? 

A) Rs. 6000 B) Rs. 3600
C) Rs. 2160 D) Rs. 415
 
Answer & Explanation Answer: C) Rs. 2160

Explanation:

End of first year     :  10000 x (3/5) = Rs. 6000
End of second year :  6000 x (3/5) = Rs. 3600
End of third year    :  3600 x (3/5) = Rs. 2160

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2 5572
Q:

A man reads 3/7 of a book on a day and 2/5 of the remaining, on the second day. If the number of pages still unread are 36, how many pages did the book contain ?

A) 105 B) 101
C) 98 D) 109
 
Answer & Explanation Answer: A) 105

Explanation:

Let number of pages in a book = p

According to questions

p - [3p/7 + (2/5 x 4p/7)] = 36

= p - 23p/35 = 36

=> 12p = 36 × 35

p = 105

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10 5462
Q:

 83% of 2350 = ?

A) 1889.95 B) 1912.35
C) 1875.25 D) 1950.50
 
Answer & Explanation Answer: D) 1950.50

Explanation:
83% of 2350 = ?
 
83/100 x 2350
 
=8.3 x 235
 
=1950.50
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12 5434
Q:

60 percent of 2/7 of three-fourth of a number is 2664. What is the number ?

A) 20720 B) 21352
C) 25421 D) 24150
 
Answer & Explanation Answer: A) 20720

Explanation:

Let N be the required number. 

=> 60100x27x34xN=2664  

=> N = 2664x2x7x5/9  

=> N = 20720.

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10 5426