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's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ? 

A) 10 B) 20
C) 30 D) 40
 
Answer & Explanation Answer: A) 10

Explanation:

A's Salary  = 40% of B = 40% of (25% of C) = 40/100[(52/100)*100] % of C = 10% of C.

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225 66022
Q:

If 75% of a number is added to 75, then the result is the number itself. The number is :

A) 100 B) 200
C) 300 D) 400
 
Answer & Explanation Answer: C) 300

Explanation:

Let the number be x, Then 

75% of x + 75 = x 

=> x - 75x/100 =75 

=> x =  300 .

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274 64506
Q:

A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:

A) Rs.180 B) Rs.120
C) Rs.480 D) data insufficient
 
Answer & Explanation Answer: B) Rs.120

Explanation:

Commission up to 10000 = 10000x9100 = 900 

 

Again after 10000, 

 

              Commission    :   Bonus 

                           9       :   3 

                         3x        :   x

 

 Therefore,   Bonus = 1380-900×14 = Rs. 120

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253 64497
Q:

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child recieve ?

A) 9 B) 10
C) 11 D) 12
 
Answer & Explanation Answer: A) 9

Explanation:

Let the total number of children be x. 

Then, x * (20% of x) = 405  

=> x * 20x/100 = 405 

15x2 = 405 

 

=> x=45 

 

Number of sweets received by each child = 20% of 45 = 9.

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291 60237
Q:

Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?

A) 3864 B) 4903
C) 5849 D) 6789
 
Answer & Explanation Answer: A) 3864

Explanation:

Saving  = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400 = Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.

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289 58101
Q:

In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent  thus he secured 41% votes of the total voters on the voter list. Percentage votes of the defeated candidate out of the total votes casted is:

A) 47.5% B) 41%
C) 38% D) 45%
 
Answer & Explanation Answer: D) 45%

Explanation:

Let there be x voters and k votes goes to loser then 

 

      0.8x - 120 = k + (k + 200)

 

         k+200 = 0.41x

 

 => k = 1440

 

and  (k + 200) =1640

 

Therefore  1440/3200 x 100 = 45%

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304 56375
Q:

A number is decreased by 10% and then increased by 10%.  The number so obtained is 10 less than the original number. What was the oiginal number ? 

A) 1000 B) 2000
C) 3000 D) 4000
 
Answer & Explanation Answer: A) 1000

Explanation:

Let the original number be x.

 

Final number obtained = 110% of (90% of x) =(110/100 * 90/100 * x) = (99/100)x. 

 

x-(99/100)x=10

=> x =1000

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145 48712
Q:

If A's height is 40% less than that of B, how much percent B's height is more than that of A?

A) 66.66% B) 76.66%
C) 96.66% D) 86.66%
 
Answer & Explanation Answer: A) 66.66%

Explanation:

Excess of B's height over A's = [(40/(100 - 40)] x 100% =  66.66%

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