Tricks to solve Percentage Problems - PDF

Percentage is a fraction whose denominator is always 100. x percentage is represented by x%.

Calculation of Percentage

If we have to find y% of x, then

Calculation of Percentage

1. To express x% as a fraction : 

We know
x% = x/100
Thus 10% = 10/100 (means 10 parts out of 100 parts)
= 1/10 (means 1 part out of 10 parts)

2. To express x/y as a percentage :

We know that x/y  = (x/y× 100 )
    Thus 1/4 = ( 1/4 ×100 )% = 25%
    and 0.8 = ( 8/10 ×100 )% = 80%

    3. To increase a number by a given percentage(x%): 

    Multiply the number by the following factor
     increase a number by a given percentage

    4. To decrease a number by a given percentage(x%): 

    Multiply the number by the following factor
    To decrease a number by a given percentage

    5. To find the % increase of a number:

    To find the % increase of a number

    6. To find the % decrease of a number:

    To find the % decrease of a number:

    Some Observation

    #1 

    If 20% candidate failed in an exam then observations are
    • 80% represent passed in exam
    • 100% represent total appeared in exam
    • (80%-20%) = 60% represent difference between passed and failed candidate in exam
    percentage

    #2

     If a number is increased by 25% then observations are 
    • 100% represent the old number
    • 125% represent the new number.

    percentage concept

    #3

     Remember that Base in the given sentence (Question) is always 100%
    Eg. Income of Ram is increased by 20% 
    In this sentence 
    100% - represent the income of Ram
    20% - represent increment
    120% - represent new income of Ram.

    Remember it :

    1 = 100%
    1/2 = 50%
    1/3 = 33 1/3%
    1/4 = 25%
    1/5 = 20%
    1/6 = 162/3%
    1/7 = 142/7%
    1/8 = 121/2%
    1/9 = 111/3%
    1/10 = 10%
    1/11 = 91/11%
    1/10 = 81/3%
    1/13% = 79/13%
    percentage problems
    25% = 1/4
    6.25% = 1/16
    125% = 5/4
    150% = 3/2
    200% = 2
    350% = 7/2

    #4

    If of A is equal to y% of B then -
    If of A is equal to y% of B then -
    Example: - If 10% of A is equal to 12% of B, then 15% of A is equal to what percent of B?
    percentages

    #5

    If A is more than B,
    percentage tricks
    Example: - If income of Ravi is 20% more than that of Ram, then the income of Ram is how much percent less than that of Ravi?
    percentage tricks

    #6

    If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then–
    percentage tricks problems
    Example: - Pankaj Sharma has to score 40% marks to get through. If he gets 40 marks and fails by 40, then find the total marks set for the examination?
    percentage tricks problems examples

    #7

    If a candidate scores marks and fails by a marks while an another candidate scores y% marks and gets b marks more than minimum passing marks, then –
    percentage tricks problems examples


    Example: - Raj scores 30% and fails by 60 marks, while Rohan who scores 55% marks, gets 40 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination?
    percentage problems examples

    #8

    If due to decrement in the price of an item, a person can buy Kg more in y rupees, then actual price of that item -
    percentage problems examples
    Example: - Ram can buy 5 Kg more sugar in rupees 100 as the price of sugar has decreased by 10%. Find the actual price of the sugar?
    percentage problems examples

    #9

    If in an election, a candidate got of total votes cast and still lose by y votes, the total number of votes cast –
    percentage problems examples
    Example: - In an election contested by two candidates, one candidate got 40% of total votes and still lost by 500 votes, find the total number of votes casted?
    percentage problems examples

    #10

    If the population of a town is P and it increases or decreases at the rate of R% per annum then –
    I. Population after ‘n’ years :
    percentage population

    II. Population ‘n’ years ago :
    percentage population
    Example: - The population of a town is 352800. If it increases at the rate of 5% per annum, then what will be its population after 2 years and 2 years ago?
    percentages

    #11

    If the value of a number is first increased by and again decreased by the net effect is always decreased by x2/100%
    Example: -The salary of a worker is first increased by 5% and then it is decreased by 5%. What is the change in his salary?

    percentages

    Examples

    #1 

    Q. If the difference between 62% of a number and 3/5th of that number is 36. what is the number ?
    Sol:
    Let the number be x.
    Then x × 62% - x × 3/5 = 36
    x ×62% -x V 60% = 36 (60% = 3/5)
    x ×2% = 36
    x ×2/100 =36
    x = 36 ×100/2 = 1800

    #2

    Q. 40% of Ram's income Rs. 1200 Then Find 
    1. 75% of Ram's income ?
    2. 1/4 part of Ram's income ?
    3. 1/3 part of Ram's income ?
    Sol :
    (1)
    40% = 1200 Rs.
    75% = 1200/40 ×75 = 2250 Rs.

    Trick : 1200 / 40  × 75 = Rs. 2250/-


    (2)
    40% of income = Rs. 1200
    Then 1/4 part (i.e. 25% ) of Ram's
    income = 1200/40 ×25 
    = Rs. 750/- Ans

    (3)
    40% of Ram's income
    = Rs. 1200
    i.e. 2/5 part of Ram's income
    = Rs. 1200
    Then total income of Ram 
    = Rs. 1200 ×5/2
    1/3 part of Ram's income
    = Rs. 1200  × 5/2  × 1/3 
    = Rs. 1000 Ans.

    Trick :

    1200/2/5  × 1/3
    = 1200/2 × 5/3 = 1000




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