Discount


  1. A bicycle, marked at ₹ 2,000, is sold with two successive discount of 20% and 10%. An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is
    1. ₹ 1,368
    2. ₹ 1,468
    3. ₹ 1,568
    4. ₹ 1,668

  1. View Hint View Answer Discuss in Forum

    Single equivalent discount for two successive discounts of 20% and 10%

    = 28 + 10 −
    20 × 10
    % = 28%
    100

    Now , single discount for 28% and 5%
    = 28 + 5 −
    28 × 5
    %
    100

    = (33 – 1.4) % = 31.6%
    ∴  Required selling price of bicycle at cash payment = (100 – 31.6) % of ₹ 2000

    Correct Option: A

    Single equivalent discount for two successive discounts of 20% and 10%

    = 28 + 10 −
    20 × 10
    % = 28%
    100

    Now , single discount for 28% and 5%
    = 28 + 5 −
    28 × 5
    %
    100

    = (33 – 1.4) % = 31.6%
    ∴  Required selling price of bicycle at cash payment = (100 – 31.6) % of ₹ 2000
    ∴  Required selling price of bicycle at cash payment =
    2000 × 68.4
    = ₹ 1368
    100


  1. An article listed at ₹ 800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price ?
    1. ₹ 620
    2. ₹ 600
    3. ₹ 640
    4. ₹ 680

  1. View Hint View Answer Discuss in Forum

    Effective discount

    = 25 + 15 −
    25 × 15
    100

    = 40 – 3.75 = 36.25 %
    ∴  CP for buyer = (100 – 36.25) % of 800
    =
    63.75 × 800
    = ₹ 510
    100

    ∴  To gain 20%,
    SP = ₹
    120 × 510
    = ₹ 612
    100

    Let the list price be ₹ P.
    ∴  90% of P = ₹ 612

    Correct Option: D

    Effective discount

    = 25 + 15 −
    25 × 15
    100

    = 40 – 3.75 = 36.25 %
    ∴  CP for buyer = (100 – 36.25) % of 800
    =
    63.75 × 800
    = ₹ 510
    100

    ∴  To gain 20%,
    SP = ₹
    120 × 510
    = ₹ 612
    100

    Let the list price be ₹ P.
    ∴  90% of P = ₹ 612
    ⇒ 
    90P
    = 612 ⇒ P =
    61200
    10090

    = ₹ 680



  1. A dealer buys a car listed at ₹ 200000 at successive discounts of 5% and 10%. If he sells the car for 179550, then his profit is
    1. 10%
    2. 9%
    3. 5%
    4. 4%

  1. View Hint View Answer Discuss in Forum

    As we know the formula for Equivalent discount for two successive discount.

    Equivalent discount =   10 + 5 −
    10 × 5
    = 14.5%
    100

    Alternate method to solve this question :
    According to given question, Marked Price = 200000, Selling Price is Cost Price for Buyer.
    D1 = 5%,
    D2 = 10%
    Selling Price = Marked Price
    100 − D1
    100 − D2
    100100

    = 200000
    100 − 5
    100 − 10
    100100

    Correct Option: C

    As we know the formula for Equivalent discount for two successive discount.

    Equivalent discount =   10 + 5 −
    10 × 5
    = 14.5%
    100

    ∴  C P (for buyer) = 85.5% of ₹ 200000
    = ₹
    85.5 × 200000
    = ₹ 171000
    100

    Selling Price = ₹ 179550
    Profit = ₹ (179550 – 171000) = ₹ 8550
    ∴  Gain % =
    8550
    × 100 = 5%
    171000

    Alternate method to solve this question :
    Here, Marked Price = 200000, Selling Price is Cost Price for buyer.
    D1 = 5%,
    D2 = 10%
    Selling Price = Marked Price
    100 − D1
    100 − D2
    100100

    = 200000
    100 − 5
    100 − 10
    100100

    = 20 × 95 × 90 = 1800 x 95
    Cost Price for buyer = 171000
    Selling Price for buyer = 179550
    Profit =
    Selling Price − Cost Price
    × 100%
    C.P.

    =
    8550
    × 100 = 5%
    171000


  1. A shopkeeper gives two successive discounts on an article marked ₹ 450. The first discount given is 10 percent. If the customer pays ₹ 344.25 for the article, the second discount given is
    1. 14 %
    2. 10 %
    3. 12 %
    4. 15 %

  1. View Hint View Answer Discuss in Forum

    Let the second discount be D2 %.
    According to the question,

    344.25 = 450 ×
    100 − 10
    ×
    100 − D2
    100100


    Alternate method to solve this question :
    Here, M.P. = Rs. 450, S.P. = Rs. 344.25, D1 = 10%, D2 = ?
    S.P. = M.P.
    100 − D1
    100 − D2
    100100

    344.25 = 450 ×
    100 − 10
    100 − D2
    100100


    Correct Option: D

    Let the second discount be D2 %.
    According to the question,

    344.25 = 450 ×
    100 − 10
    ×
    100 − D2
    100100

    ∴  100 − D2 =
    344.25 × 100 × 100
    450 × 90

    ∴  100 – D2 = 85
    ∴  D2 = 100 – 85 = 15%.
    Alternate method to solve this question :
    Here, M.P. = Rs. 450, S.P. = Rs. 344.25, D1 = 10%, D2 = ?
    S.P. = M.P.
    100 − D1
    100 − D2
    100100

    344.25 = 450 ×
    100 − 10
    100 − D2
    100100

    3442500
    = (100 − D2)
    450 × 90

    34425
    = (100 − D2)
    45 × 9

    3825
    = (100 − D2)
    45 × 1

    425
    = (100 − D2)
    5 × 1

    ⇒  85 = 100 – D2
    ⇒  D2 = 15 %



  1. A person paid ₹ 17,000 for a motor-car after a single discount of 15%. If he is given successive discounts of 5% and 10% then how much he would pay ?
    1. ₹ 17,000
    2. ₹ 17,010
    3. ₹ 17,100
    4. ₹ 18,900

  1. View Hint View Answer Discuss in Forum

    Let M be the marked price.
    Single Discount = 15%
    ⇒  100 – 15 = 85 %
    85% of M = 17,000

    Required SP = 20,000 ×
    95
    ×
    90
    100100


    Alternate method to solve this question :
    M.P =
    S.P. × 100
    100 − D

    M.P =
    17000 × 100
    100 − 15

    M.P =
    17000 × 100
    85

    Correct Option: C

    Let M be the marked price.
    Single Discount = 15%
    ⇒  100 – 15 = 85
    85% of M = 17,000

    ∴  M =
    17,000
    × 100
    85

    M = ₹ 20,000
    Required SP = 20,000 ×
    95
    ×
    90
    100100

    Required SP = 180 × 95 = ₹ 17100
    Alternate method to solve this question :
    M.P =
    S.P. × 100
    100 − D

    M.P =
    17000 × 100
    100 − 15

    M.P =
    17000 × 100
    85

    M.P. = 20000

    S.P = M.P.
    100 − D1
    100 − D2
    100100

    S.P = 20000
    100 − 5
    100 − 10
    100100

    S. P = 20000 ×
    95
    ×
    90
    100100

    S.P = 180 × 95 = ₹ 17100