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, % .

Thus, % = 25%;  



II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is%

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is%



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 = 

2. Population n years ago =  



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 = 

2. Value of the machine n years ago = 



V. If A is R% more than B, then B is less than A by            


If A is R% less than B , then B is more than A by  



In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :

A) 2500 B) 2700
C) 2900 D) 3100
Answer & Explanation Answer: B) 2700


Total number of votes = 7500

Given that 20% of Percentage votes were invalid

=> Valid votes = 80%

Total valid votes = 

1st candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes

=> Valid votes that 2nd candidate got = total valid votes x 

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264 45575

If 20% of a = b, then b% of 20 is the same as :

A) 4% of a B) 6% of a
C) 8% of a D) 10% of a
Answer & Explanation Answer: A) 4% of a


20% of a = b   

b% of 20 = = = = 4% of a.

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122 29906

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?

A) 20 B) 30
C) 40 D) 50
Answer & Explanation Answer: C) 40


The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water.so remaining 32% is fruit content. weight of fresh fruits is 100kg

Dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.

fruit % in freshfruit = fruit% in dryfruit

(32/100) * 100 = (80/100 )* y

we get, y = 40 kg

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219 28747

A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.


Let x be the maximum marks, 

Then (25% of x)+30 = (50% of x)-20

\inline \Rightarrow \inline \frac{x}{4}+30 = \frac{x}{2}-20

\inline \Rightarrow 2x-x=120+80 \Rightarrow x=200

Hence maximum marks = 200

Minimum pass marks = \inline \frac{200}{4}+30=80

Hence, minimum pass marks = \inline \frac{80}{200}\times 100=40%

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96 27457

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :

A) 10000 B) 12000
C) 14000 D) 16000
Answer & Explanation Answer: B) 12000


= Rs.12000

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116 19247