Banker's Discount

Banker's Discount

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  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 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. What rate per cent does Shantanu get for his money in discounting a bill due 30 months hence he deducts 30% of the amount of the bill ?








  1. View Hint View Answer Discuss in Forum

    Let the amount of the bill = ₹ 100.
    Money deducted = ₹ 30
    Money received by the holder of the bill = ₹ (100 - 30) = ₹ 70
    SI on ₹ 70 for 30 months = ₹ 30
    ∴ Rate = [100 x 30] / [70 x (30/12)]% per annum

    Correct Option: D

    Let the amount of the bill = ₹ 100.
    Money deducted = ₹ 30
    Money received by the holder of the bill = ₹ (100 - 30) = ₹ 70
    SI on ₹ 70 for 30 months = ₹ 30
    ∴ Rate = [100 x 30] / [70 x (30/12)]% per annum
    = (10 x 3 x 12) / 21 %
    = (10 x 12) / 7 %
    = 120/7 %
    = 171/7 %

  1. The true discount on a certain sum due 1 yr hence at 30% per annum, is ₹ 240. What is the banker' discount on the same sum for the same time and at the same rate ?








  1. View Hint View Answer Discuss in Forum

    We know that
    BG = SI on TD = (240 x 30 x 1 x 1)/100 = ₹ 72
    Again, BG = BD - TD
    ⇒ BD = BG + TD

    Correct Option: C

    We know that
    BG = SI on TD = (240 x 30 x 1 x 1)/100
    = ₹ 72
    BG = BD - TD
    ⇒ BD = BG + TD
    = 72 + 240
    = ₹ 312

  1. The true discount on a bill of Rs. 1860 due after 8 months is Rs. 60. Find the banker's gain ?








  1. View Hint View Answer Discuss in Forum

    P.W. = Rs. 1860 - Rs. 60 = Rs. 1800
    ∴ B.G. = (T.D.)2/P.W.

    Correct Option: D

    P.W. = Rs. 1860 - Rs. 60 = Rs. 1800
    ∴ B.G. = (T.D.)2/P.W. = (60 x 60)/1800 = Rs. 2