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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:

A man’s average monthly expenditure for the first four months of the year was Rs. 231.25. For the next five months, the average monthly expenditure was Rs. 22.75 more than what it was during the first four months. If the person spent Rs. 605 in all during the remaining three months of the year, find what percentage of his annual income of Rs. 3500 did he save in the year?

A) 10% B) 15%
C) 20% D) 25%
 
Answer & Explanation Answer: C) 20%

Explanation:

A man's average monthly expenditure for the first four months of the year = Rs.231.25.
For four month = 231.25 * 4 = Rs. 925
For next five month he spend = 231.25 + 22.75 for one month.
In five month he spend = (231.25 + 22.75) X 5 = 1270
If the person spent Rs. 605 in all during the remaining three months of the year,
Total expense = 925+1270+605= 2800
Saving = 3500-2800 = 700
% saving = 700/3500 * 100 = 20%

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Q:

In a test, 14% of the students failed in Maths and 22% failed in Hindi. If 18% of the students failed in both the subjects, then the percentage of students who passed in both the subjects is

A) 46 B) 44
C) 42 D) 40
 
Answer & Explanation Answer: A) 46

Explanation:

Let the number of students = 100

Number of students who failed in one or more subjects = 14 + 22 + 18 = 54%

The percentage of students who passed in both the subjects = 100 - 54 = 46%.

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Q:

A woman suffered 20% loss on first investment and made 10% profit at second investment and 12 ½% profit on the third investment. If the invested amount be in the ratio of 4 : 5 : 3, find her profit percentage?

A) 0.625% B) 1.205%
C) 0.987% D) 0%
 
Answer & Explanation Answer: A) 0.625%

Explanation:

From the given data,

let the amounts invested be 4p, 5p and 3p

Net profit = Total profit - Total loss

= 10x5p/100 + 25x3p/200 - 20x4p/100

= 0.875p - 0.8p

= 0.075p

Therefore, profit% = (Net profit/Total investment) x 100

= 0.075 x 100/12 

= 0.0625%

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Q:

If the side of square is increased by 6%, then what will be the percentage increase in its area?

A) 3.2 B) 12.04
C) 12.12 D) 12.36
 
Answer & Explanation Answer: D) 12.36

Explanation:
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Q:

The costs of daily ticket of local train is Rs 160 and Monthly Pass costs Rs 2912. If I buy the Monthly Pass and travel for 26 days in a month then I save?

A) 25 percent B) 22 percent
C) 18 percent D) 30 percent
 
Answer & Explanation Answer: D) 30 percent

Explanation:
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Q:

Twenty percent of Karthik’s monthly salary is equal to thirty two percent of Nikitha’s monthly salary. Vipin’s monthly salary is four fifth that of Nikitha’s monthly salary. If Vipin’s annual salary is Rs. 3.84 lakhs, what is Karthik’s monthly salary?

A) 32,000 B) 64,000
C) 40,000 D) 52,000
 
Answer & Explanation Answer: B) 64,000

Explanation:

From the given data,

20% of K = 32% of N

V = 4/5 N

 

Given Vipin's salary = 3.84 lpa = 3.84/12 = 32,000 per month

Now, N = 5/4 x 32000 = 40000

Now K = 32/20 x 40000 = 64000

 

Hence, karthik's monthly salary = Rs. 64000.

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Q:

In a city of engineers of 4800, the number of female engineers are 3/8th of them. The number of female engineers is what percentage of the number of male engineers?

A) 76 B) 60
C) 56 D) 52
 
Answer & Explanation Answer: B) 60

Explanation:

Total engineers = 4800

Number of female engineers = 3/8 x 4800 = 1800

Then, number of male engineers = 4800 - 1800 = 3000

Now, required is female engineers is what percentage of the number of male engineers

=> 1800 is what % of 3000

=> p x 3000/100 = 1800

=> 30p = 1800

p = 60%

 

Hence, female engineers is 60 percentage of the number of male engineers.

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Q:

What is 6% of 3,50,000?

A) 19500 B) 21000
C) 23600 D) 24000
 
Answer & Explanation Answer: B) 21000

Explanation:

6% of 350000

 

6100 x 3,50,000= 6 x 3500= 21,000.

 

Hence, 6% of 3,50,000 = 21,000.

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