Tricks to Solve Problems on Percentage

  1. 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 = 1 .
    100 5
    To express a as a percent: We have, a = a x 100 %.
    b b b
        Thus, 1 = 1 x 100 % = 25%.
    4 4
  2. Percentage Increase/Decrease:If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
    R x 100 %
    (100 + R)

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

    R x 100 %
    (100 – R)
  3. Results on Population:Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
    1. Population after n years = P 1 + R n
    100
    2. Population n years ago = P
    1 + R n
    100
  4. Results on Depreciation:Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
    1. Value of the machine after n years = P 1 – R n
    100
    2. Value of the machine n years ago = P
    1 – R n
    100
    3. If A is R% more than B, then B is less than A by R x 100 %.
    (100 + R)
    4. If A is R% less than B, then B is more than A by R x 100 %.
    (100 – R)
    A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
    A. 45%
    B.
    45 5 %
    11
    C.
    54 6 %
    11
    D. 55%

    Answer: Option B

    Explanation:

    Number of runs made by running = 110 – (3 x 4 + 8 x 6)

    = 110 – (60)

    = 50.

     Required percentage = 50 x 100 % = 45 5 %
    110 11
    Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
    A. 39, 30
    B. 41, 32
    C. 42, 33
    D. 43, 34

    Answer: Option C

    Explanation:

    Let their marks be (x + 9) and x.

    Then, x + 9 = 56 (x + 9 + x)
    100

     25(x + 9) = 14(2x + 9)

     3x = 99

     x = 33

    So, their marks are 42 and 33.

    A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

    What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

    If A = x% of y and B = y% of x, then which of the following is true?

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

    Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

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