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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 number X is mistakenly divided by 10 instead of being multiplied by 10. What is the percentage error in the result?

A) -99% B) +99%
C) -100% D) +100%
 
Answer & Explanation Answer: A) -99%

Explanation:

By mistake = x/10 

 

Actual value = x * 10 

 

% Change = 10x-x1010x×100 = 99100×100  = 99% (negative)

 

Since actual value is greater than the wrong value.

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15 15592
Q:

A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets ?

A) 40% B) 45%
C) 50% D) 55%
 
Answer & Explanation Answer: C) 50%

Explanation:

Number of runs made by running = 120 - (3 x 4 + 8 x 6) = 120 - (60) = 60 

Required percentage = [(60/120)*100] % = 50%

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30 15463
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 15295
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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21 15082
Q:

Read the data given and answer the following questions

 

In a class of 60 students:

 

42 like Maths,

32 like English,

12 like neither Maths nor English

 

How many students like exactly one subject?

A) 16 B) 12
C) 6 D) 22
 
Answer & Explanation Answer: D) 22

Explanation:
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0 14974
Q:

Read the data given below and answer the questions based on it.

 

In the CBSE Board exams last year, 53% passed in Biology, 61% percent passed in English, 60% in Social studies, 24% in Biology and English, 35% in English and social studies, 27% in Biology and social studies and 5% in none.

 

If the number of students in the class is 200, how many passed in only one subject?

A) 48 B) 46
C) More than 50 D) Less than 40
 
Answer & Explanation Answer: B) 46

Explanation:
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3 14912
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 14788
Q:

If price of rice increased by 25%, so that a man is can able to purchase 5 kg less rice in Rs. 500. Find the original price of rice per kg ?

A) Rs. 20 B) Rs. 24
C) Rs. 26 D) Rs. 29
 
Answer & Explanation Answer: A) Rs. 20

Explanation:

Let the original price of rice be Rs. x

Let rice a man can buy for Rs. 500 at rs. x/kg be = R kgs

From given data, for Rs. 500

x ---- R kgs

(x + 25x/100) ---- (R - 5) kgs

=> Rx = (R - 5)(x + 25x/100)

=> Rx = (R - 5)(125x/100)

=> 100Rx = 125Rx - 625x

=> R = 25

So at rate of Rs. x/kg, man get 25 kgs for Rs. 500

=> x = 500/25 = Rs. 20

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21 14570