Discount


  1. If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :
    1. $ 20
    2. $ 21.81
    3. $ 22
    4. $ 18.33

  1. View Hint View Answer Discuss in Forum

    Given :- Amount = $ 110
    S.I. on $ (110 - 10) for a given time = $ 10
    S.I. on $ 100 for double the time = $ 20
    Sum = $ (100 + 20) = $ 120

    ∴ True discount = Amount x Rate x Time
    100 + Rate x Time

    Correct Option: D

    Given :- Amount = $ 110
    S.I. on $ (110 - 10) for a given time = $ 10
    S.I. on $ 100 for double the time = $ 20
    Sum = $ (100 + 20) = $ 120

    ∴ True discount = Amount x Rate x Time
    100 + Rate x Time

    T.D. on $ 110 = $ 20 x 110= $ 18.33
    120


  1. A trader marks his goods at 20% above the cost price. If he allows a discount of 5% for cash down payment, his profit percent for such a transaction is
    1. 15%
    2. 12%
    3. 14%
    4. 17%

  1. View Hint View Answer Discuss in Forum

    Let C.P. be ₹ 100.
    Marked price = ₹ 120

    S.P. =
    120 × 95
    = ₹ 114
    100

    Gain percent = 14%
    2nd method to solve this question.
    Here, r = 20%, r1 = 5%
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Correct Option: C

    Let C.P. be ₹ 100.
    Marked price = ₹ 120

    S.P. =
    120 × 95
    = ₹ 114
    100

    Gain percent = 14%
    2nd method to solve this question.
    Here, r = 20%, r1 = 5%
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Gain % =
    20 × (100 − 5)
    − 5
    100

    Required Gain % = 19 – 5 = 14%



  1. A merchant marks his goods 40% above the cost price and sells them at a discount of 15%. Find his gain %.
    1. 25%
    2. 22%
    3. 19%
    4. 20%

  1. View Hint View Answer Discuss in Forum

    Let the C.P. of each article be ₹ 100.
    ∴  Marked price = ₹ 140

    ∴  S.P. =
    140 × 85
    = ₹ 119
    100

    ∴  Gain percent = 19%
    2nd method to solve this question.
    Here, r = 40%, r1 = 15%
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Correct Option: D

    Let the C.P. of each article be ₹ 100.
    ∴  Marked price = ₹ 140

    ∴  S.P. =
    140 × 85
    = ₹ 119
    100

    ∴  Gain percent = 19%
    2nd method to solve this question.
    Here, r = 40%, r1 = 15%
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Gain % =
    40 × (100 − 15)
    − 15
    100

    Gain % =
    40 × 85
    − 15
    100

    Gain % =
    3400
    − 15
    100

    Required Gain % = 19%


  1. Maha Bazaar offers 20% discount on bags which have been marked 50% above the cost price. Amarnath pays ₹ 840 for a bag. Then the cost price of the bag is
    1. ₹ 672
    2. ₹ 700
    3. ₹ 790
    4. ₹ 810

  1. View Hint View Answer Discuss in Forum

    Let the cost price be ₹ 100.
    ∴  Marked price = ₹ 150

    S.P. =
    150 × 80
    = ₹ 120
    100

    when S.P. = 120, C.P. = 100
    when S.P. = 840
    C.P. =
    100
    × 840 = ₹ 700
    120

    2nd method to solve this question.
    Here, r = 50%, r1 = 20%,
    S.P. = ₹ 840
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Correct Option: B

    Let the cost price be ₹ 100.
    ∴  Marked price = ₹ 150

    S.P. =
    150 × 80
    = ₹ 120
    100

    when S.P. = 120, C.P. = 100
    when S.P. = 840
    C.P. =
    100
    × 840 = ₹ 700
    120

    2nd method to solve this question.
    Here, r = 50%, r1 = 20%,
    S.P. = ₹ 840
    Gain % =
    r ×(100 − r1)
    − r1
    100

    Gain % =
    50 × (100 − 20)
    − 20
    100

    Gain % =
    50 × 80
    − 20
    100

    Gain % = 20%
    We know that ,
    Gain % =
    S.P. − C.P.
    × 100
    C.P.

    20 =
    840 − p
    × 100
    p

    20p= 84000 – 100p
    120p = 84000
    p = 700
    ∴  C.P. = ₹ 700



  1. A trader marks his goods 40% above cost price and allows a discount of 25 %. The profit he makes, is :
    1. 15%
    2. 10 %
    3. 5 %
    4. 2 %

  1. View Hint View Answer Discuss in Forum

    Let the cost price be ₹ 100.
    Marked price = ₹ 140

    S.P.=
    75 × 140
    = ₹ 105
    100

    ∴  Profit percent = 5%
    2nd method to solve this question.
    Here, r = 40%, r1 = 25%
    Profit % =
    r ×(100 − r1)
    − r1
    100

    Correct Option: C

    Let the cost price be ₹ 100.
    Marked price = ₹ 140

    S.P.=
    75 × 140
    = ₹ 105
    100

    ∴  Profit percent = 5%
    2nd method to solve this question.
    Here, r = 40%, r1 = 25%
    Profit % =
    r ×(100 − r1)
    − r1
    100

    =
    40 × (100 − 25)
    − 25
    100

    =
    40 × 75
    − 25
    100

    =
    3000
    − 25
    100

    Profit % = 30 – 25 = 5%