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 bag contains 600 coins of 25 p denomination and 1200 coins of 50 p denomination. If 12% of 25 p coins and 24% of 50 p coins are removed, the percentage of money removed from the bag is nearly :

A) 21.6 % B) 15.3 %
C) 14.6 % D) 12.5 %
 
Answer & Explanation Answer: A) 21.6 %

Explanation:

Total money = Rs.[600*(25/100)+1200*(50/100)]= Rs. 750.

 

25 paise coins removed = Rs. (600*12/100) = 72.

 

50 paise coins removed = Rs. (1200*24/100)= 288.

 

Money removed =Rs.(72*25/100+288*50/100)  = Rs.162.

 

Required percentage = (162/750*100)% = 21.6 %.

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63 27736
Q:

How many litres of pure acid are there in 8 litres of a 20% solution ?

A) 1.4 B) 1.5
C) 1.6 D) 1.7
 
Answer & Explanation Answer: C) 1.6

Explanation:

Quantity of pure acid = 20% of 8 litres = ((20/100)*8) litres = 1.6 litres.

 

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44 27083
Q:

Two numbers are 20% and 30% less than the third number . How much percent is the second number less than first?

Answer

Let the third number be 100.


 


Then, the first number = 100 - 20 = 80 and second number = 100 - 30 = 70.


 


Difference between the first and second number = 80-70 = 10


 


\inline \therefore Required percentage = 1080 x 100% = 100/8 = 12.5%


 


 

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43 26540
Q:

A student multiplied a number by 2/5 instead of 5/2. What is the percentage error in evaluation ?

A) 52% B) 64%
C) 84% D) 77%
 
Answer & Explanation Answer: C) 84%

Explanation:

Let the number be 'x'

 

Then, according to the given data,

 52x-25x52xx100

 

2125x100

 

= 84%

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18 25966
Q:

The sum of the number of boys and girls in a school is 150. if the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is : 

A) 60 B) 70
C) 80 D) 90
 
Answer & Explanation Answer: A) 60

Explanation:

We have : x + (x% of 150 )= 150 

=> x+(x/100)*150] = 150

=> 52x = 150  

=> x = (150*2)/5 = 60

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47 25786
Q:

In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10 kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was : 

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

Explanation:

Let the original quantity be x kg. Vanaspati ghee in x kg  =  (40x / 100 )kg = (2x / 5) kg. 

Now, (2x/5)/(x + 10) = 20/100

=> 2x / (5x + 50) = 1/5 

=> 5x = 50 

=> x = 10.

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56 25783
Q:

The diference of two numbers is 20% of the larger number, if the smaller number is 20, then the larger number is :

A) 15 B) 25
C) 35 D) 45
 
Answer & Explanation Answer: B) 25

Explanation:

Let the large number be x.

Then x - 20 = 20x/100

=> x - x/5 = 20  => x = 25.

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59 25531
Q:

 The difference between a number and its two-fifth is 510. What is 10% of that number ?

A) 75 B) 85
C) 95 D) 105
 
Answer & Explanation Answer: B) 85

Explanation:

Let the number be x. Then, x-(2/5)x = 510

=> 3x/5 =510 

=>x =[510 * ( 5/3)] =850 

10 % 0f 850 = 85.

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45 24503