Discount


  1. The marked price of a radio is ₹ 4,800. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent will be
    1. 18%
    2. 20%
    3. 22%
    4. 25%

  1. View Hint View Answer Discuss in Forum

    Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
    Let CP of radio be Rs. y.
    According to the question,

    108y
    = 4800 ×
    90
    = 4320
    100100

    ⇒  y =
    4320 × 100
    = ₹ 4000
    108

    Gain = 4800 - 4000 = ₹ 800
    If no discount is allowed,then
    Gain percent =
    800
    × 100 = 20%
    4000

    Second method :
    Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
    With the help of given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    Correct Option: B

    Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
    Let CP of radio be Rs. y.
    According to the question,

    108y
    = 4800 ×
    90
    = 4320
    100100

    ⇒  y =
    4320 × 100
    = ₹ 4000
    108

    Gain = 4800 - 4000 = ₹ 800
    If no discount is allowed,then
    Gain percent =
    800
    × 100 = 20%
    4000

    Second method :
    Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
    With the help of given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    4800
    =
    100 + 8
    C.P.100 − 10

    C.P. =
    4800 × 90
    = 4000
    108

    Gain % (without discount) =
    4800 − 4000
    × 100
    4000

    Gain % =
    800
    × 100 = 20%
    4000


  1. After allowing a discount of 16%, there was still a gain of 5%. Then the percentage of marked price over the cost price is
    1. 15%
    2. 18%
    3. 21%
    4. 25%

  1. View Hint View Answer Discuss in Forum

    Let the C.P. of article be ₹ 100 and its marked price be y.
    Discount = 16% and gain = 5%

    ∴  y ×
    84
    = 105
    100

    ⇒  y =
    105 × 100
    = 125
    84

    Difference = 125 - 100 = 25
    ∵ C.P. of article = ₹ 100
    ∴  Required percentage = 25%
    Second method to solve this question :
    Here, r = 5% , D = 16%
    Using the given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    Correct Option: D

    Let the C.P. of article be ₹ 100 and its marked price be y.
    Discount = 16% and gain = 5%

    ∴  y ×
    84
    = 105
    100

    ⇒  y =
    105 × 100
    = 125
    84

    Difference = 125 - 100 = 25
    ∵ C.P. of article = ₹ 100
    ∴  Required percentage = 25%
    Second method to solve this question :
    Here, r = 5% , D = 16%
    Using the given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    M.P.
    =
    100 + 5
    =
    105
    C.P.100 − 1684

    Required Percentage =
    105 − 84
    × 100 = 25%
    84



  1. A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be
    1. 56.25%
    2. 25.56%
    3. 50.25%
    4. 54.25%

  1. View Hint View Answer Discuss in Forum

    Let the marked price = ₹ 100
    ∴  S.P after discount of 20% = ₹ 80
    Profit = 25%

    ∴  CP = ₹
    100
    ×80= ₹ 64
    125

    Profit after selling on marked price= 100 – 64 = ₹ 36
    ∴  Gain % =
    36
    × 100 = 56.25%
    64

    Second method to solve this question :
    Here, D = 20%,r = 25%
    Let, M.P. be ₹ 100
    M.P.
    =
    100 + r
    C.P.100 − D

    Correct Option: A

    Let the marked price = ₹ 100
    ∴  S.P after discount of 20% = ₹ 80
    Profit = 25%

    ∴  CP = ₹
    100
    ×80= ₹ 64
    125

    Profit after selling on marked price= 100 – 64 = ₹ 36
    ∴  Gain % =
    36
    × 100 = 56.25%
    64

    Second method to solve this question :
    Here, D = 20%,r = 25%
    Let, M.P. be ₹ 100
    M.P.
    =
    100 + r
    C.P.100 − D

    100
    =
    100 + 25
    C.P.100 − 20

    C.P. =
    100 × 80
    = ₹ 64
    125

    Profit = 100 – 64 = 36
    Gain % =
    36
    × 100% = 56.25%
    64


  1. In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit per cent of
    1. 30%
    2. 32%
    3. 33%
    4. 35%

  1. View Hint View Answer Discuss in Forum

    Given in question , discount = 10%
    Let the marked price be ₹ 100.
    ∴  S.P. = 90% of 100 = ₹ 90
    Profit = 17%

    C.P.= ₹ 90 ×
    100
    117

    C.P. = ₹
    1000
    13

    If no discount is allowed, S.P. = ₹ 100
    Profit = ₹100 −
    1000
    = ₹
    300
    1313

    ∴  Profit % =
    ( 300 / 13 )
    × 100 = 30%
    ( 1000 / 13 )

    Second method :
    Here, D = 10%, r = 17%,
    Let the M.P. = ₹ 100
    With the help of given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    Correct Option: A

    Given in question , discount = 10%
    Let the marked price be ₹ 100.
    ∴  S.P. = 90% of 100 = ₹ 90
    Profit = 17%

    C.P.= ₹ 90 ×
    100
    117

    C.P. = ₹
    1000
    13

    If no discount is allowed, S.P. = ₹ 100
    Profit = ₹100 −
    1000
    = ₹
    300
    1313

    ∴  Profit % =
    ( 300 / 13 )
    × 100 = 30%
    ( 1000 / 13 )

    Second method :
    Here, D = 10%, r = 17%,
    Let the M.P. = ₹ 100
    With the help of given formula ,
    M.P.
    =
    100 + r
    C.P.100 − D

    100
    =
    100 + 17
    C.P.100 − 10

    100
    =
    117
    C.P.90

    C.P. =
    100 × 90
    =
    1000
    11713

    Profit = S.P. – C.P.
    Profit = 100 −
    1000
    13

    Profit = Rs.
    300
    13

    Profit % =
    ( 300 / 13 )
    × 100 = 30%
    ( 1000 / 13 )



  1. The price that Akbar should mark on a pair of shoes which costs him ₹ 1,200 to gain 12% after allowing a discount of 16% (in rupees) is
    1. 1,344
    2. 1,433
    3. 1,600
    4. 1,500

  1. View Hint View Answer Discuss in Forum

    Given that , Cost price of pair of shoes = ₹ 1,200 , Gain = 12%
    Let the marked price be y.

    ∴  y ×
    84
    =
    1200 × 112
    100100

    = y ×
    80
    = 112 × 12
    400

    ⇒  y =
    112 × 1200
    = ₹ 1600
    84

    Second method :
    Given Here , C.P. = ₹ 1200, r = 12%, D = 16%
    M.P.
    =
    100 + r
    C.P.100 − D

    Correct Option: C

    Given that , Cost price of pair of shoes = ₹ 1,200 , Gain = 12%
    Let the marked price be y.

    ∴  y ×
    84
    =
    1200 × 112
    100100

    = y ×
    80
    = 112 × 12
    400

    ⇒  y =
    112 × 1200
    = ₹ 1600
    84

    Second method :
    Given Here , C.P. = ₹ 1200, r = 12%, D = 16%
    M.P.
    =
    100 + r
    C.P.100 − D

    M.P.
    =
    100 + 12
    1200100 − 16

    M.P. =
    112 × 1200
    = ₹ 1600
    84