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    Percentage Tricks and formulas

    Percentage Important Aptitude Formulas:

    (I). Concept of Percentage:
    1. 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.

    2. Percentage increase = (increase/original) × 100

    3. Percentage decrease = (decrease/original) × 100

    4. Increased value at rate of x% after time‘t’ be
                     Increased value = Present value × [(100 + x)/100]t
                     Decreased value = Present value × [(100 - x)/100]t

    5. Initial value that is increased to present value at the rate of x% in time t, then
                  Initial value = present value × [100/(100 + x)]t

    6. Initial value that is decreased to present value at the rate of x% in time t, then
                  Initial value = present value × [100/(100 - x)]t

    (II) 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 = P × [1 + (R/100)]n
         2. Population n years ago = P/[1 + (R/100)]n

    (III). 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 = P × [1 - (R/100)]n
         2. Value of the machine n years ago = P/[1 - (R/100)]n

    (IV). 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]%.





    Example: 01
    If the sales tax reduced from 3½ % to 3⅓ %, then what difference does it make to a person who purchases an article with market price of Rs. 8400?

    Solution:
     Required difference = [3½ % of Rs.8400] – [3⅓ % of Rs.8400]
    = [(7/2) - (10/3)] % of Rs.8400 =1/6 % of Rs.8400
    = Rs. [(1/6) × 8400] × (1/100) = Rs. 14.


    Example: 02
    A man calculates that if he lets his house for Rs 80 per month, he would earn 7½ % p.a on his outlay after allowing for repairs. Actually he is able to let it for Rs. 76 p.m and had to spend Rs. 60 more on repairs. He thus gets only 6% p.a on his outlay. Find the outlay?

    Solution: Let, price of the outlay is x.
    Therefore, 1½ % of x = (4 × 12) + 60
    or,     (3/2) × (x/100) = 108
    or,     x = 7200

    Percentage Aptitude:
    Formula:                Percentage Aptitude Formulas
    Solved Examples:  Solved Examples: Set 01
    Practice Test:         Practice Test: 01     Practice Test: 02
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    Item Reviewed: Percentage Tricks and formulas Rating: 5 Reviewed By: Pranab Debnath
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