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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:

30% of a number is 33. What is the number?

 

A) 120 B) 115
C) 105 D) 110
 
Answer & Explanation Answer: D) 110

Explanation:
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Q:

Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?

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

Explanation:

20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.

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10 12422
Q:

The average of a set of whole numbers is 27.2. when the 20% of the elements are eliminated from the set of numbers then the average become 34. The number of elements in the new set of numbers can be :

A) 27 B) 35
C) 52 D) 63
 
Answer & Explanation Answer: C) 52

Explanation:

only (c) is correct since it is divisible by 4.

 

Let the original number of element  be x then the new no.of elements will be 

 

            4x5 = K                               

 

So K must be divisible by 4

 

Since,      x =  Kx5/4

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12 12405
Q:

A number increased by 30% gives 390. The number is

A) 180 B) 300
C) 480 D) 260
 
Answer & Explanation Answer: B) 300

Explanation:

Let the number be 'N'
Given N + 30N/100 = 390
=> 130N/100 = 390
=> N = 390 x 10/13
=> N = 300.

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16 12154
Q:

600 students took the test on physics and chemistry. 35% students failed in physics and 45% students failed in chemistry and 40% of those who passed in chemistry also passed in physics, then how many students failed in both:

A) 162 B) 138
C) 60 D) None of these
 
Answer & Explanation Answer: D) None of these

Explanation:

                  Physics             Chemistry

Failed           35%                    45%

Passed         65%                    55%

Passed in both = 22% of total student

percentage of students who are passed in any of the physics or chemistry or both =(65+55) - 22 = 98%

So, the percentage of students who are failed in both = 2%

Therefore, total failed (in both subjects) students = 12 

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14 11955
Q:

The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference  in the expenditure on that product?

A) 10% more B) 5% more
C) 12.5% more D) 17.5% more
 
Answer & Explanation Answer: C) 12.5% more

Explanation:

    Quantity  X  Rate =  Price

 

         1  x  1  =  1

 

       0.7 x 1.25 = 0.875

 

      Decrease in price = (1-0.875) x 100 = 12.5%

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18 11705
Q:

Two numbers are respectively 40% and 30% more than a third number. The second number expressed in terms of percentage of the first is ?

A) 92.8% B) 84.23%
C) 87.14% D) 94.1%
 
Answer & Explanation Answer: A) 92.8%

Explanation:

Here, x = 40 and y = 30;
Therefore second number
= [[100+y100+x] x 100 ]% of first number
= [[100+y100+x] x 100 ]% of first number
Second number = 92.8% of the first number.

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12 11672
Q:

5% people of a village in India died by dengue, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning ?

A) 4400 B) 3100
C) 2800 D) 5600
 
Answer & Explanation Answer: A) 4400

Explanation:

Let 'P' be the original population at the beginning

P x (95/100) x (85/100) = 3553

P = 4400.

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