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Percentage problems tricks(SSC,BANK,PO)


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

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)

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%

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

    [ R/(100+R)×100 ] %

    If the price of a commodity decreases by R%, then the increase in consumption as not to decrease the expenditure is -

    [ R/(100-R)×100 ] %

    Result on Population : 

    Let the population of a town be P now and suppose increases the rate of R% per annum, then :
    1. Population after n years = P ( 1+ R/100 )n 
    2. Population  n years ago = P /( 1+ R/100 )n 

    Result on Depreciation : 

    Let the present value of a machine be P. Suppose depreciates at the rate of R% per annum Then :
    1. Value of the machine after n Years 
     = P ( 1- R/100 )n 
    2. Value of the machine n years ago
    = P /( 1- R/100 )n 
    • If A is R% more than B, then B is less than A by
    [ R/(100+R)×100 ]%
    If A is R% less than B, then B is more than A by
    [ R/(100-R)×100 ]%
    • Net % change = x + y + xy/100

    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

    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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