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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 an item is decreased by 25%. What percent increase must be done in new price to get the original price?

A) 33.33% B) 43.3%
C) 50% D) 55.3%
 
Answer & Explanation Answer: A) 33.33%

Explanation:

Let the price of an item be 100After 25% decrease, price of item = 75Increase in price to get the original price = 100-75 = 25% increase to get the original price = 25/75 X 100 = 100/3 = 33.33%

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Q:

A man spend 20% of his monthly salary on his children's education and 50% of his salary on food and transport. After Paying the rent of Rs.1000, he is left with Rs.2000. What is his monthly salary?

A) 7000 B) 10000
C) 14000 D) 20000
 
Answer & Explanation Answer: B) 10000

Explanation:

Let his monthly salary be 'P'

20% on children's education = 20P100 = P5

50% on food and transport = 50P100 = P2

1000 on rent

=> P - P5 - P2 - 1000 = 2000=> 3P = 30000=> P = 10000

 

Therefore, his monthly salary = Rs. 10,000

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Q:

Express 6.72 % in ratio ?

A) 65 : 124 B) 42 : 625
C) 21 : 125 D) 37 : 442
 
Answer & Explanation Answer: B) 42 : 625

Explanation:

6.72/100 = 672/10000 = 42/625

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Q:

Last year vivek saved 10% of his annual earnings, this year he earned 5% more than last year and he saved 12% of his annual earnings. The amount saved this year was what percentage of the amount saved last year ?

A) 87% B) 98%
C) 138% D) 126%
 
Answer & Explanation Answer: D) 126%

Explanation:

Suppose total earnings = Rs. 10000
10% saving = 10000 x (10/100) = Rs. 1000
This year 5% more income than prev year = Rs. 10500
12% saving = 10500 x (12/100) = Rs. 1260
Percentage of amount saved = (1260/1000) x 100 = 126%

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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) 860 D) 760
 
Answer & Explanation Answer: A) 1060

Explanation:

From the given data,

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

= 960 + 100

= 1060.

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Q:

Prashanth sold a album for $ 735 and made a profit of 22.5% . The cost price of the album went up by $120 and so Prashanth increased the selling price by $120. What is his profit % now ?

A) 19.32 % B) 18.75 %
C) 21.41 % D) 22 %
 
Answer & Explanation Answer: B) 18.75 %

Explanation:

Prashanth sold a album for $ 735 and made a profit of 22.5% .
CP = 735 x 100/122.5 = Rs. 600
New CP = 600 + 120 = Rs. 720
New SP = 735 + 120 = Rs. 855.

Profit = Rs. 135.

profit % = 100 x 135/720 = 18.75%.

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Q:

P, Q and R secured 45%, 50% and 60% marks respectively in Biology. M’s marks in Biology is 12.5 more than P’s marks and 4 less than R’s marks. Find out the individual marks of four students.

 

A. For the students, total marks obtained for Biology is 311.5.
B. Total of M’s and P’s marks in Biology is 147.5.
C. R has obtained 84 marks.

A) Only C B) Only A & B
C) All are required D) None of the statements is required
 
Answer & Explanation Answer: D) None of the statements is required

Explanation:

From the given data,
(60 - 45)% = 12.5 + 4
15% = 16.5
=> 100% = ?
100% = 16.5 x 100/15 = 110

Hence, P = 45% of 110 = 45x110/100 = 49.5
Q = 50% of 110 = 55
R = 60% of 110 = 60 x 110/100 = 66
M = 12.5 + 49.5 = 62 or 66 - 4 = 62

 

Hence, no statement is required to answer.

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Q:

Subbu purchased a tape recorder at 9/10 of its selling price and sold it at 8% more than its selling price. His gain is

Answer

Let S.P = x then C.P = \inline \frac{9x}{10}


Selling price received by subbu = (108% of x)


                                            = \inline \frac{108}{100}x=\frac{27}{25}x


Gain= \inline (\frac{27}{25}x-\frac{9}{10}x)=\frac{9}{50}x


Hence gain% = \inline (\frac{9x}{50}\times \frac{10}{9x}\times 100) = 20%

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