Percentage : Types of Questions Asked in Competitive Exams

Hello Friends, In this chapter we will go through various " types of questions asked in competitive exams " on percentage in aptitude section.

Type 1 : Problems based on numbers

Question 1. A number on subtracting 35 to it reduces it by 80 %. What is the 20 % of that number ?

Solution : Let the number be X
According to Question,
X - 35 = X ( 80/100 )
=> X - 35 = 8 X / 10
=> 10 X - 350 = 8 X
=> 10 X - 8 X = 350
=> 2 X = 350
=> X = 175
Now, 20 % of 175 = ( 20 /100 ) 175 = 35

Type 2 : Problem based on Students and Marks

Under this, there are two different ways by which questions can be asked in the examination.

Way 1 : A candidate scores x % is an examination fails by ‘a’ marks, while another candidate who scores y % marks and get 'b' marks more than the maximum required passing marks, then the maximum marks for the examination is given by

M = {100 ( a + b ) / ( y - x )}

Question 2 : In a quarterly examination a student secured 30% marks and failed by 15 marks. In the same examination another student secured 40% marks and got 35 marks more than minimum marks to pass. Calculate the maximum marks and the passing marks.

Solution : Maximum marks ( M ) = { 100 ( 15 + 35 ) / ( 40 - 30 ) } = 5000 / 10 = 500

Passing Marks = 30 % of 500 + 15 or 40 % of 500 - 35

Way 2 : In an examination a % of total number of candidates failed in a subject X and b % of total number of candidates failed in subject Y and c % failed in both subjects, then percentage of candidates, who passed in both the subjects, is [100 – (a + b – c)] %

Question 3 : In an examination, 42 % of the candidates failed in English and 52 % failed in Mathematics. If 17 % failed in both the subjects, then find the percentage of candidates who passed in both the subjects.

Solution : Percentage of candidates, who passed in both the subjects, is [100 – (a + b – c)] %

Thus, Percentage of candidates, who passed in both the subjects = [ 100 - ( 42 + 52 - 17 ) ] % = 23 %

Type 3 : Problems based on Depreciation

Question 4 : The value of a printing machine depreciates at the rate of 20 % per annum. If the cost of machine at present is Rs. 60,000, then what will be its worth after 2 years ?

Solution : In this type of problem we will use the formula 

Price of goods after n years = Present Price { 1 - ( Rate / 100 ) } ⁿ

Thus, Price of printing machine after 2 years = 60000 { 1 - ( 20 / 100 ) } ²

= 60000 { 4 / 5 } ² = 60000 ( 16 / 25 ) = 38400

Type 4 : Problem based on population

Under this, there are two different ways by which questions can be asked in the examination.

Way 1 : If the current population of a city is X and the rate of increase in population is Y then population after n years is given by formula : X { 1 + ( Y / 100 )  } ⁿ

Question 5 : The current population of a city is 60000. Find the population of city after 2 years if the rate of increase in population is 20 %.

Solution : Population after 2 years = 60000 { 1 + ( 20 / 100 ) } ²

= 60000 { 6 / 5 } ² = 60000 ( 36 / 25 ) = 86400

Way 2 : If the current population of a city is X and the rate of increase in population is Y then population n years ago is given by formula : X / { 1 + ( Y / 100 )  } ⁿ

Question 6 : The current population of a city is 60000. Find the population of city 2 years ago if the rate of increase in population is 20 %.

Solution : Population 2 years ago = 60000 / { 1 + ( 20 / 100 ) } ²

= 60000 / { 6 / 5 } ² = 60000 / ( 36 / 25 ) = 41667

Type 5 : Problem based on price of goods or services

Under this, there are two different ways by which questions can be asked in the examination.

Way 1 : If the price of goods increases by R %, then the reduction in consumption so as not to increase the expenditure can be calculated using the formula :

{ R / ( 100 + R) } x 100 %

Question 7 : The price of diesel increases by 25 %. Find by how much percent a truck owner must reduce his consumption in order to maintain the same budget ?

Solution : { 25 / ( 100 + 25 ) } x 100 % = 20 %

Way 2 : If the price of goods decreases by R %, then the increase in consumption so as not to decrease the expenditure can be calculated using the formula :

{ R / ( 100 - R) } x 100 %

Question 8 : The price of rice falls by 25 %. By what percentage a person can increase the consumption of rice so that his overall budget does not change ?

Solution : { 25 / ( 100 - 25 ) } x 100 % = 33.33 %

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