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:

If K earns 12% less than L, then how much percent more does L earn than K ?

A) 13.96% B) 13.63%
C) 13.56% D) 14.01%
 
Answer & Explanation Answer: B) 13.63%

Explanation:

Required % is given by 

 

=> 12100-12x100

 

= 1200/88

 

= 13.636%

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9 3653
Q:

Due to increase of 33.33% in the price of apples, a customer can purchase 4 apples less for Rs 16. What is the original price (in paise) of an apple?

A) 100 B) 125
C) 150 D) 400/3
 
Answer & Explanation Answer: A) 100

Explanation:
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Q:

A man wills 40% of his wealth to his wife and rest to his children. What percent of the wealth willed to the wife do the children get?

A) 150 B) 66.6
C) 50 D) 20
 
Answer & Explanation Answer: A) 150

Explanation:
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2 3556
Q:

1 bottle of honey costs Rs 240 but a pack of 4 of the same bottles costs Rs 768. What is the effective discount (in %) on the pack?

A) 16 B) 25
C) 10 D) 20
 
Answer & Explanation Answer: D) 20

Explanation:
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0 3546
Q:

16 of 225 is =

A) 7.11 B) 7.21
C) 6.87 D) 7.58
 
Answer & Explanation Answer: A) 7.11

Explanation:

16 of 225 is = 

16 = p × 225100p = 1600225 = 7.1111

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9 3534
Q:

5% of 40,000 is

A) 20000 B) 2000
C) 200 D) 20
 
Answer & Explanation Answer: B) 2000

Explanation:

5% of 40,000  = 5100 × 40,000 = 5 × 400 = 2,000  

 

Hence, 5% of 40,000 = 2,000.

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7 3436
Q:

In a hostel the rent per room is increased by 20%. If number of rooms in the hostel is also increased by 20% and the hostel is always full, then what is the percentage change in the total collection at the cash counter?

A) 30% B) 40%
C) 44% D) 48%
 
Answer & Explanation Answer: C) 44%

Explanation:
Let initial rent be rs 10
And initial rooms be 10
So initial collection = 10*10 = Rs 100
Now new rent = 10 + 20% of 10 = 12
New no of rooms = 10 + 20% of 10 = 12
So new collection = 12*12 = 144
% change in collection = (144-100)/100*100 = 44%
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4 3414
Q:

29 is 0.8% of?

A) 3625 B) 1450
C) 7250 D) 10875
 
Answer & Explanation Answer: A) 3625

Explanation:
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