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:

What percent of 7.2 kg is 18 gms ?

A) .25% B) .5%
C) .75% D) 1%
 
Answer & Explanation Answer: A) .25%

Explanation:

Required percentage = (18/7200 * 100)% =  1/4% = 0.25%

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192 47119
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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108 44533
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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50 39537
Q:

270 candidates appeared for an examination, of which 252 passed. The pass percentage is :

A) (91 + 1/3)% B) (93 + 1/3 )%
C) (97 + 1/3 )% D) (98 + 1/3) %
 
Answer & Explanation Answer: B) (93 + 1/3 )%

Explanation:

Pass percentage  =[(252/270)*100] % =280/3 % =9313 9 %

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111 37703
Q:

The ratio 5 : 4 expressed as a percent equals :

A) 12.5 % B) 40 %
C) 80 % D) 125 %
 
Answer & Explanation Answer: D) 125 %

Explanation:

5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

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155 37288
Q:

Ram sell his goods 25% cheaper than Shyam and 25% dearer than Bram. How much % is Bram's good cheaper than Shyam ?

A) 60% B) 40%
C) 50% D) 30%
 
Answer & Explanation Answer: B) 40%

Explanation:

Lets say shyam sells at 100,

 

Since Ram sells 25% cheaper than Shyam,

 

Therefor Ram sells at less than 25% of100 or 75 rs.

 

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

 

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

 

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

 

Hence Brams Good is 40% cheaper than that of Shyam's good.

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77 34647
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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43 34522
Q:

If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by

A) 15 B) 20
C) 25 D) 30
 
Answer & Explanation Answer: B) 20

Explanation:

Let original consumption = 100 kg and new consumption = x kg, 

So, 100 * 6 = x * 7.50 => x = 80kg 

Reduction in consumption = 20%.

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109 34486