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 3124
Q:

12% of 70,000 is

A) 8400 B) 7200
C) 6000 D) 5600
 
Answer & Explanation Answer: A) 8400

Explanation:

12% of 70,000

=> 12 x 70,000/100

=> 8400

 

Hence, 12% of 70,000 = 8,400

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3 3113
Q:

In a class of 80 students and 5 teachers, each student got sweets that are 15% of the total number of students and each teacher got sweets that are 25% of the total number of students. How many sweets were there?

A) 1060 B) 960
C) 1020 D) 920
 
Answer & Explanation Answer: A) 1060

Explanation:

Total number of sweets

= 80 x 15 x 80/100 + 5 x 80 x 25/100

= 960 + 100 = 1060

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31 3089
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 3071
Q:

The percentage of metals in a mine of zinc ore is 60%. Now the percentage of silver is 3/4% of metals and the rest is zinc. If the mass of ore extracted from the mine is 8000 kg, the mass (in kg) of zinc is

A) 5147 kg B) 4764 kg
C) 3587 kg D) 2125 kg
 
Answer & Explanation Answer: B) 4764 kg

Explanation:

Mass of zinc ore = 8000 kg


Mass of metal = 60% of 8000 = 4800 kg


Mass of silver in metal = 3/4 x 4800/100 = 36 kg


Mass of zinc = 4800 - 36 = 4764 kg.

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4 3065
Q:

Rohan spends 24% of an amount of money on an insurance policy, 34% on food, 19% on children’s education and 17% on recreation. He deposits the remaining amount of Rs. 540 in bank. How much total amount does he spend on food and insurance policy together?

A) Rs. 6350 B) Rs. 5220
C) Rs. 5890 D) Rs. 6458
 
Answer & Explanation Answer: B) Rs. 5220

Explanation:

Remaining % of amount with Rohan

= 100 - (24 + 34 + 17 + 19)

= 100 - 94

= 6%

=> 6% = 540

=> 100% = ?

540 x 100/6 = Rs. 9000

Now, Money spent on insurance and food is

= 34 + 24 = 58% of 9000

= 58 x 9000/100

= 58 x 90

= Rs. 5220

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5 3047
Q:

A man wills 25% of his wealth to charity and rest to his family. What percent of the wealth willed to charity does the family get?

A) 200 B) 33.3
C) 300 D) 25
 
Answer & Explanation Answer: C) 300

Explanation:
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3 3015
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 3012