Banker's Discount


  1. The banker’s gain on a certain sum due 2.5 years hence is 9/25 times of the banker’s discount. What is the rate percent?









  1. View Hint View Answer Discuss in Forum

    Let the banker’s discount, BD = Rs. 1

    Then, banker’s gain, BG =
    9
    × 1 = Rs.
    9
    2525

    BG = BD − TD
    9
    = 1 − TD
    25

    ⇒ TD = 1 −
    9
    =
    16
    2525

    F = BD ×
    TD
    BD − TD

    = 1 ×
    16
    25
    1 −
    16
    25


    Correct Option: D

    Let the banker’s discount, BD = Rs. 1

    Then, banker’s gain, BG =
    9
    × 1 = Rs.
    9
    2525

    BG = BD − TD
    9
    = 1 − TD
    25

    ⇒ TD = 1 −
    9
    =
    16
    2525

    F = BD ×
    TD
    BD − TD

    = 1 ×
    16
    25
    1 −
    16
    25

    =
    16
    25
    9
    25

    = Rs.
    16
    9

    BD = Simple Interest on the face value of the bill for unexpired time
    =
    FTR
    100

    ⇒ 1 =
    16
    x
    5
    x
    R
    92100

    ⇒ R = 100 ×
    9
    = 22
    1
    %
    402


  1. A bill is discounted at 10 % per annum. If banker’s discount is allowed, at what rate % should the proceeds be invested so that nothing will be lost?









  1. View Hint View Answer Discuss in Forum

    Let the amount = Rs. 100 Then BD = Rs. 10 ( ∵ banker’s discount, BD is the simple Interest on the face value of the bill for unexpired time and bill, in this case, is discounted at 10% per annum)
    Proceeds = Rs. 100 − Rs. 10 = Rs. 90
    Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost.
    As we know the Simple interest formula,

    ⇒ Simple interest =
    Principal × Time × Rate of Interest
    100

    As per given question,
    Simple interest = 10,
    Principle amount = 90
    Time = 1 year
    Rate of interest = R

    Correct Option: B

    Let the amount = Rs. 100 Then BD = Rs. 10 ( ∵ banker’s discount, BD is the simple Interest on the face value of the bill for unexpired time and bill, in this case, is discounted at 10% per annum)
    Proceeds = Rs. 100 − Rs. 10 = Rs. 90
    Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost.
    As we know the Simple interest formula,

    ⇒ Simple interest =
    Principal × Time × Rate of Interest
    100

    As per given question,
    Simple interest = 10,
    Principle amount = 90
    Time = 1 year
    Rate of interest = R
    ⇒ 10 = 90 × 1 ×
    R
    100

    ⇒ R = 11
    1
    %
    9



  1. A banker paid Rs. 5767.20 for a bill of Rs. 5840, drawn of April 4 at 6 months. If the rate of interest was 7 %, what was the day on which the bill was discounted?









  1. View Hint View Answer Discuss in Forum

    As per given question,
    Face Value F = 5840
    Banker discount BD = Face Value - Paid by banker = 5840 - 5767.20 = 72.8
    Rate of interest = 7 %
    As we know the formula,

    BD =
    F x T x R
    100

    ⇒ 72.8 =
    5840 × T × 7
    100

    Correct Option: D

    As per given question,
    Face Value F = 5840
    Banker discount BD = Face Value - Paid by banker = 5840 - 5767.20 = 72.8
    Rate of interest = 7 %
    As we know the formula,

    BD =
    F x T x R
    100

    ⇒ 72.8 =
    5840 × T × 7
    100

    ⇒ T = 13 ×
    365
    days = 65 days
    73

    ⇒ Unexpired Time = 65 days
    ⇒ Given that Date of Draw of the bill = 4th April at 6 months ⇒ 4th October
    ⇒ Legally Due Date = (4th October + 3 days) = 7th October
    Hence, The date on which the bill was discounted
    = (7th October − 65 days) = 3rd August


  1. Shankara buys a watch for Rs. 1,950 in cash and sells it for Rs. 2,200 at a credit of 1 year. If the rate of interest is 10% per annum, he _____ :









  1. View Hint View Answer Discuss in Forum

    As per given question,
    Amount A = 2200
    Rate of Interest R = 10 %
    Time = 1 year
    S.P. = P.W. of Rs. 2200 due 1 year hence

    Principle Amount = Rs.
    A x 100
    100 + ( R x T )

    Correct Option: B

    As per given question,
    Amount A = 2200
    Rate of Interest R = 10 %
    Time = 1 year
    S.P. = P.W. of Rs. 2200 due 1 year hence

    Principle Amount = Rs.
    A x 100
    100 + ( R x T )

    Principle Amount = Rs.
    2200 x 100
    100 + ( 10 x 1 )

    Principle Amount = Rs.
    2200 x 100
    110

    Principle Amount = Rs. 20 x 100 = Rs. 2000
    ∴ Gain = Rs. (2000 − 1950) = Rs. 50.



  1. A bill for Rs. 3000 is drawn on 14th July at 5 months. It is discounted on 5th October at 10 %. What is the Banker’s Discount BD?









  1. View Hint View Answer Discuss in Forum

    As per the given all information in above question , we have
    Date on which the bill is drawn = 14th July at 5 months i.e., Nominally Due Date = 14th December
    Legally Due Date = 14th December + 3 days = 17th December
    Date on which the bill is discounted = 5th October

    ⇒ Unexpired Time = 73 Days = 1 year
    5

    Banker's Discount = Simple Interest on the face value of the bill for unexpired time
    Banker's Discount = FTR
    100

    Here , F = 3000 , T = 1 / 5 year , Rate = 10%

    Correct Option: A

    As per the given all information in above question , we have
    Date on which the bill is drawn = 14th July at 5 months i.e., Nominally Due Date = 14th December
    Legally Due Date = 14th December + 3 days = 17th December
    Date on which the bill is discounted = 5th October

    ⇒ Unexpired Time = 73 Days = 1 year
    5

    Banker's Discount = Simple Interest on the face value of the bill for unexpired time
    Banker's Discount = FTR
    100
    Here , F = 3000 , T = 1 / 5 year , Rate = 10%
    Banker's Discount =3000 × 1 x 10 = Rs. 60
    5100