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 Percentage Questions

Popular Latest Rated Important Formulae

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:

The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of

A) 45% B) 40%
C) 35% D) 32.5%
 
Answer & Explanation Answer: B) 40%

Explanation:

Let the original price of the cycle be 100. After the first reduction the price will be 75.

This new price is then reduced by 20% = 0.8 x 75 = 60

60 represents a reduction of 40 percent on the original.

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18 14104
Q:

Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ?

A) 10.769 % B) 11.23 %
C) 10.4 % D) 9.87 %
 
Answer & Explanation Answer: A) 10.769 %

Explanation:

I      II     III

65   58   100

65 -------- 7
100 ------ ?  => 10.769%

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12 13398
Q:

In an examination a candidate got 30% marks and failed by 30 marks. If the passing marks are 60% of the total marks, then the maximum marks will be: 

A) 450 B) 600
C) 300 D) 100
 
Answer & Explanation Answer: D) 100

Explanation:

Passing marks are 0.6x 

 

so 0.3x + 30 = 0.6x   => x = 100

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19 13394
Q:

A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?

A) 0.75D B) 0.76D
C) 0.765D D) None of the above
 
Answer & Explanation Answer: C) 0.765D

Explanation:

If the price is reduced by 15 %, then the new price will be 0.85D

If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D

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12 13263
Q:

In a factory there are three types of Machines M1 , M2 and M3 which produces 25%, 35% and 40% of the total products respectively. M1, M2 and M3 produces 2% , 4% and 5% defective products, respectively. What is the percentage of non-defective products?

A) 89% B) 97.1%
C) 96.1% D) 86.1%
 
Answer & Explanation Answer: C) 96.1%

Explanation:

Non- defective products

 

25x0.98+35x0.96+40x0.95100 x 100 = 96.1

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22 13175
Q:

What should come in place of question mark (?) in the following question?

45% of 400+ √? = 56% of 750 - 40% of 350

A) 10000 B) 1000
C) 10201 D) 9801
 
Answer & Explanation Answer: A) 10000

Explanation:

45/100×400+√?=56/100 ×750 -40/100 ×350

180 + √? = 420 - 140 180 + √? = 280 √? = 280 - 180 √? = 100 ? = 1002 ? = 10000

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0 13061
Q:

A number, when 35 is subtracted from it, reduces to its 80 percent. What is four - fifth of that number  ?

A) 175 B) 140
C) 135 D) 95
 
Answer & Explanation Answer: B) 140

Explanation:

x - 35 = 80x/100 

=> x = 175 

=> 4x/5 = 4x175/5 = 140.

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18 12783
Q:

A Shopkeeper  charges sales tax of x% upto Rs.2,000 and above it he charges y%. A customer pays total tax of Rs 320, when he purchases the goods worth Rs. 6,000 and he pay's the total tax of Rs. 680 for the goods worth Rs. 12,000. The value of (x-y) is:

A) 0 B) -2
C) -4 D) 5
 
Answer & Explanation Answer: B) -2

Explanation:

          2000xX100 + 4000xY100 = 320

 

and     2000xX100 + 10000xY100 = 680

 

x = 4  and  y = 6

 

x-y = -2

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14 12699