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:

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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349 68000
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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355 65645
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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171 65288
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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263 64974
Q:

40% of 75 + 80% of 25 = K% of 250

 

Find the value of K?

A) 10 B) 20
C) 30 D) 35
 
Answer & Explanation Answer: B) 20

Explanation:

From the given data,

 

40100 x 75 + 80100 x 25 = K100 x 25030 + 20 = 5K250 x 2 = 5KK = 1005 = 20

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21 57643
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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232 55715
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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109 53425
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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