Discount


  1. The marked price of a watch is 800. A shopkeeper gives two successive discounts and sells the watch at 612. If the first discount is 10%, the second discount is :
    1. 10%
    2. 12%
    3. 15%
    4. 20%

  1. View Hint View Answer Discuss in Forum

    Let the second discount be D2 %.
    Then, 90 % of (100 – D2) % of 800 = 612

    ⇒ 
    90
    ×
    100 − D2
    × 800 = 612
    100100


    Another method to solve :
    Here, M.P. = Rs. 800, S.P. = Rs. 612, D1 = 10%, D2 = ?
    S.P. = M.P.
    100 − D1
    100 − D2
    100100

    612 = 800 ×
    100 − 10
    100 − D2
    100100

    612 = 800 ×
    90
    ×
    100 − D2
    100100

    Correct Option: C

    Let the second discount be D2 %.
    Then, 90 % of (100 – D2) % of 800 = 612

    ⇒ 
    90
    ×
    100 − D2
    × 800 = 612
    100100

    ⇒  100 − D2 =
    612 × 100
    = 85
    90 × 8

    ⇒  D2 = 100 – 85 = 15%
    Another method to solve :
    Here, M.P. = Rs. 800, S.P. = Rs. 612, D1 = 10%, D2 = ?
    S.P. = M.P.
    100 − D1
    100 − D2
    100100

    612 = 800 ×
    100 − 10
    100 − D2
    100100

    612 = 800 ×
    90
    ×
    100 − D2
    100100

    6120
    = 100 × D2
    72

    D2 =
    100 − 6120
    72

    D2 =
    7200 − 6120
    = 15%
    72


  1. The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately the price of the article is
    1. increased by 10%
    2. increased by 5.3%
    3. decreased by 3%
    4. decreased by 5.3%

  1. View Hint View Answer Discuss in Forum

    Let us assume the original price be ₹ 100
    ∴  Increased price = ₹ 130

    Equivalent discount = 10 + 10 −
    10 × 10
    = 10 + 10 - 1 = 19 %
    100

    Correct Option: B

    Let us assume the original price be ₹ 100
    ∴  Increased price = ₹ 130

    Equivalent discount = 10 + 10 −
    10 × 10
    = 10 + 10 - 1 = 19 %
    100

    ∴  Ultimate price of the article = ( 100 - 19 )% of 130 = 81 % of 130 = 105.3
    i.e. increase by 5.3%.



  1. The marked price of a watch was ₹ 720. A man bought the same for ₹ 550.80, after getting two successive discounts, the first at 10 %. What was the second discount rate?
    1. 12%
    2. 14%
    3. 15%
    4. 18%

  1. View Hint View Answer Discuss in Forum

    Marked price = ₹ 720
    Actual price = ₹ 550.80
    First discount D1 = 10 %
    Let the second discount = D2 %
    As we know the formula,

    Successive discounts of D1 % and D2 % is overall equals to = 10 + D2
    10 × D2
    %
    100

    = 10 + D2
    10 × D2
    100

    = 10 + D2
    D2
    10

    2nd Method :
    Here, Marked price = ₹ 720
    Selling price = ₹ 550.80
    First discount D1 = 10 %
    Let assume the second discount = D2 %
    As we know the formula,
    Selling Price = Market Price
    100 − D1
    100 − D2
    100100

    550.80 = 720
    100 − 10
    100 − D2
    100100

    ⇒  550.80 = 720 ×
    90
    ×
    100 - D2
    100100


    Correct Option: C

    Marked price = ₹ 720
    Actual price = ₹ 550.80
    First discount D1 = 10 %
    Let the second discount = D2 %
    As we know the formula,

    Successive discounts of D1 % and D2 % is overall equals to = 10 + D2
    10 × D2
    %
    100

    = 10 + D2
    10 × D2
    100

    = 10 + D2
    D2
    10

    = 10 + D2 - 0.1D2
    = 10 + 0.9D2
    According to question,
    720 x ( 100 - 10 - 0.9D2) % = 550.80
    ⇒  720 x ( 90 - 0.9D2) = 550.80 x 100
    ⇒  90 - 0.9D2 =
    55080
    720

    ⇒  90 - 0.9D2 =
    5508
    72

    ⇒  90 - 0.9D2 =
    612
    8

    ⇒  0.9D2 = 90 -
    612
    8

    ⇒  0.9D2 =
    720 - 612
    8

    ⇒  0.9D2 =
    108
    8

    ⇒  0.9D2 =
    27
    2

    ⇒  D2 =
    27
    × 0.9
    2

    ⇒  D2 = 27 ×
    10
    × 9
    2

    ⇒  D2 = 3 ×
    10
    =
    30
    22

    ∴  Second discount = 15%

    2nd Method to solve this question.
    Here, Marked price = ₹ 720
    Selling price = ₹ 550.80
    First discount D1 = 10 %
    Let assume the second discount = D2 %
    As we know the formula,
    Selling Price = Market Price
    100 − D1
    100 − D2
    100100

    550.80 = 720
    100 − 10
    100 − D2
    100100

    ⇒  550.80 = 720 ×
    90
    ×
    100 - D2
    100100

    ⇒  550.80 = 72 ×
    9
    ×
    100 - D2
    1100

    ⇒  550.80 = 72 × 9 x
    (100 - D2)
    100

    ⇒  550.80 x 100 = 72 × 9 x ( 100 - D2 )
    ⇒  55080 = 648 x ( 100 - D2 )
    ⇒  55080 = 648 x 100 - 648 x D2
    ⇒  55080 = 64800 - 648 x D2
    ⇒  648 x D2 = 64800 - 55080
    ⇒  648 x D2 = 9720
    ⇒  D2 =
    9720
    648

    ⇒  D2 = 15 %