Banker's Discount

Banker's Discount

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  1. The banker's gain on a certain sum due 21/2 years hence is (3/23)
    of the banker's discount. The rate per cent is ?








  1. View Hint View Answer Discuss in Forum

    Let B.D. be Re. 1. Then B.G. = Re. (3/23)
    ∴ T.D.= Re. (1 - 3/23) = Re. (20/23)

    Correct Option: B

    Let B.D. be Re. 1. Then B.G. = Re. (3/23)
    ∴ T.D.= Re. (1 - 3/23) = Re. (20/23)
    Sum = Rs. [(1 x 20/23 / (1 - 20/23)] = Rs. 20/3
    ∴ S.I. on Rs. 20/3 for 21/2 years is Re. 1
    ∴ Rate = (100 x 1 / 20/3 x 5/2)% = 6%

  1. Find the difference between the banker's discount and the true discount on Rs. 8100 for 3 months at 5% ?








  1. View Hint View Answer Discuss in Forum

    Difference between banker's discount and the true discount = Banker's gain.
    ⇒ B.G. = (B.D.) - (T.D.)

    B.D. = FTR / 100
    = [8100 x (1/4) x 5] / 100
    = 101.25

    T.D. = FTR / (100 + TR)
    = [8100 x (1/4) x 5] / (100 + 5/4)
    = 100

    Correct Option: B

    Difference between banker's discount and the true discount = Banker's gain.
    ⇒ B.G. = (B.D.) - (T.D.)

    B.D. = FTR / 100
    = [8100 x (1/4) x 5] / 100
    = 101.25

    T.D. = FTR / (100 + TR)
    = [8100 x (1/4) x 5] / (100 + 5/4)
    = 100

    ⇒ B.G. = 101.25 - 100
    = Rs. 1.25

  1. The banker's discount on a sum of money for 11/2 years is Rs. 60 and
    the true discount on the same sum for 2 years is Rs. 75. The rate per cent is ?








  1. View Hint View Answer Discuss in Forum

    B.D. for (3/2) years = Rs. 60
    B.D. for 2 years = Rs. (60 x 2/3 x 2) = Rs. 80
    Now, B.D. = Rs. 80; T.D. = Rs. 75
    and Time = 2 years
    ∴ Sum = Rs. (80 x 75 / 5) = Rs. 1200

    Correct Option: D

    B.D. for (3/2) years = Rs. 60
    B.D. for 2 years = Rs. (60 x 2/3 x 2) = Rs. 80
    Now, B.D. = Rs. 80; T.D. = Rs. 75
    and Time = 2 years
    ∴ Sum = Rs. (80 x 75 / 5) = Rs. 1200
    ∴ Rs. 80 is S.I. on Rs. 1200 for 2 years.
    So, rate = (100 x 80/1200 x 2)% = 31/3%B.D. for (3 / 2) years = Rs. 60
    B.D. for 2 years = Rs. (60 x 2 / 3 x 2) = Rs. 80
    Now, B.D. = Rs. 80; T.D. = Rs. 75 and Time = 2 years
    ∴ Sum = Rs. (80 x 75 / 5) = Rs. 1200
    ∴ Rs. 80 is S.I. on Rs. 1200 for 2 years.
    So, rate = (100 x 80 / 1200 x 2)% = 31/3%

  1. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain ?








  1. View Hint View Answer Discuss in Forum

    Sum = (B.D. x T.D.) / (B.D. - T.D.) = (B.D. x T.D.) / B.G.
    ∴ T.D. / B.G. = Sum / B.D. = 1650/165 = 10/1
    i.e., if B.G. is Re. 1, T.D. = Rs. 10 or B.D. = Rs. 11

    Correct Option: A

    Sum = (B.D. x T.D.) / (B.D. - T.D.) = (B.D. x T.D.) / B.G.
    ∴ T.D. / B.G. = Sum / B.D. = 1650/165 = 10/1
    i.e., if B.G. is Re. 1, T.D. = Rs. 10 or B.D. = Rs. 11
    ∴ if B.D. is Rs. 11, T.D. = Rs. 10
    If B.D. is Rs. 165, T.D. = Rs. (10/11) x 165 = Rs. 150
    Also, BG = Rs. (165 - 150) = Rs. 15

  1. The interest on a certain sum of money is Rs. 67.20 and the discount on the same of money for the same time and at the same rate is Rs. 60. What is sum ?








  1. View Hint View Answer Discuss in Forum

    Interest on Sum - True discount
    = Interest on true Discount.
    Proof Sum = P.W. + T.D.
    ∴ Interest on Sum = Interest on P.W. + Interest on T.D.
    = T.D. + Interest on T.D.
    Interest on Sum - T.D. = Interest on T.D. or Banker's gain = Int. on T.D.

    Correct Option: A

    Interest on Sum - True discount
    = Interest on true Discount.
    Proof Sum = P.W. + T.D.
    ∴ Interest on Sum = Interest on P.W. + Interest on T.D.
    = T.D. + Interest on T.D.
    Interest on Sum - T.D. = Interest on T.D. or Banker's gain = Int. on T.D.
    Rs. 67.20 - Rs. 60 = Interest on Rs. 60
    ∴ Rs. 71/5 = Interest on Rs. 60
    ∴ Re.1 = Interest on Rs. 60/71/5
    ∴ Rs. 671/5 = Interest on Rs. 60 / 71/5 x 671/5
    ∴ The required sum = Rs. 60/71/5 x 671/5 = Rs. 560