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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308 86527
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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353 85895
Q:

25% of 25% Is Equal To

 

A) 0.0625 B) 0.0210
C) 0.03145 D) 0.3210
 
Answer & Explanation Answer: A) 0.0625

Explanation:

25% of 25% means

 

 

 

25/100 of 25/100

 

 

 

i.e, 1/4 of 1/4

 

 

 

or in other words 1/4 x 1/4=1/16

 

 

 

Hence, the answer is 1/16 = 0.0625.

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88 81192
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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342 77313
Q:

56% of 225 + 20% of 150 = ? - 109

 

Find the value of '?' in the above equation

A) 264 B) 220
C) 241 D) None
 
Answer & Explanation Answer: A) 264

Explanation:

Given 56% of 225 + 20% of 150 = ? - 109

we know that a% of b = b% of a

Now,

225% of 56 + 20% of 150 = ? - 109

200% of 56 + 25% of 56 + 20% of 150 = ? - 109

112 + 14 + 30 = ? - 109

? = 112 + 14 + 30 + 109

? = 264

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57 72162
Q:

45% of 750  -  25% of 480 = ?

 

A) 337.50 B) 217.50
C) 376.21 D) 120
 
Answer & Explanation Answer: B) 217.50

Explanation:

Given expression = (45 x 750/100) - (25 x 480/100) = (337.50 - 120) = 217.50

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71 69523
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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324 68629
Q:

A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?

A) 8 B) 9
C) 10 D) 11
 
Answer & Explanation Answer: B) 9

Explanation:

Actual price = Rs. (25 + 2.50) = Rs. 27.50. 

 

Saving = 2.50

 

Percentage Saving = [(2.50/27.50)*100]

 

= 2500/275

 

9111%

 

9%

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154 67706