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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:

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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Subject: Percentage

6 7213
Q:

At an examination in which maximum marks are 500. K got 10% less than L, L got 25% more than M and M got 20% less than N. If K got 360 marks what percentage of marks was obtained by N ?

A) 80 B) 87
C) 78 D) 76
 
Answer & Explanation Answer: A) 80

Explanation:

Let marks obtained by N = x

M's marks = 0.80x

L's marks = 1.25 (0.80x)

K's marks = (0.90) (1.25) (0.80x)

= 0.9x

But 0.9x = 360 ⇒ x = 400

Percentage of Marks obtained by N

= 400 x 100/500 = 80%

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7 7194
Q:

80% of 900 + 162 x 4 x ? = 113 - 99

A) 0.5 B) 1
C) 4 D) 0
 
Answer & Explanation Answer: A) 0.5

Explanation:

80x900/100 + 256 x 4 x ? = 1331 - 99

720 + 1024 x ? = 1232

? = 1232 - 720/1024

? = 512/1024 = 0.5

? = 0.5 

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11 7159
Q:

12 as a percentage?

A) 50% B) 5%
C) 0.5% D) 0.05%
 
Answer & Explanation Answer: A) 50%

Explanation:

1/2 as a percentage means

1/2 = 0.5 in decimal

Now, in percentage means 0.5 x 100% = 50%.

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9 7149
Q:

A duster is of dimension 5x5x7 all in cms,  is sinked into a cylindrical vessel of radius 5 cm and height 10 cm. After insertion the level of the water is inccresed by 2.14 cm. Then by what percentage the part of the duster is above the layer ?

A) 96 % B) 4 %
C) 97 % D) 3 %
 
Answer & Explanation Answer: B) 4 %

Explanation:

Imension of the duster is assumed as 5x5x7 cm3

Volume of the duster below the water layer
= volume of water increased
= πxrxrxh = 3.14×52×2.14 ≈ 168 cm3

Total volume of the duster = 5×5×7 = 175 cm3

Percentage of the duster part below the layer = 168×100/175 = 96%

Percentage of the duster part above the layer = 4%

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4 7119
Q:

A merchant commences with a certain capital and gains annually at the rate of 30 per cent. At the end of 2 years he has worth Rs 10,000. What was the original capital? 

A) Rs. 4987 B) Rs. 5148
C) Rs. 5917 D) Rs. 6254
 
Answer & Explanation Answer: C) Rs. 5917

Explanation:

Let the Original capital amount be Rs. P

Given after 2 years the amount is Rs. 10000

Rate of interest = 30%

According to the question,

P x 130100 x 130100 = 10000=> P = 1000000169 = 5917

Therefore, the capital amount P = Rs. 5917

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6 7086
Q:

Which value is equal to 5% of 1,500?

A) 35 B) 55
C) 75 D) 45
 
Answer & Explanation Answer: C) 75

Explanation:

In the question it is asked for 5% of 1500

5 x 1500/100 = 15 x 5 = 75.

 

Hence, 5% of 1,500 is equal to 75.

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10 7033
Q:

If three eighth of a number is 141. What will be the approximately value of 32.08% of this number ?

A) 101 B) 112
C) 104 D) 120
 
Answer & Explanation Answer: D) 120

Explanation:

K x 3/8 = 141 => K = 376

376 x 32.08/100 = 120

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5 7009