Arithmatical - Banker's Discount

DIRECTIONS : Problems based on Banker's Discount.

1. The banker's discount on Rs.1800 at 12% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
  A.  3 months
  B.  4 months
  C.  5 months
  D.  6 months
Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 12%.
Time=(100x72 / 12x1800)
= 1/3 year
= 4 months.
2. The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.6. The true discount is
  A.  Rs.72
  B.  Rs.36
  C.  Rs.54
  D.  Rs.50
Solution
T.D = [B.G x 100 / R x T]
= Rs.(6 x 100 / 12 x 1)
= Rs.50.

3. If the true discount on a certain sum due 6 months hence at 15% is Rs.120. What is the banker's discount on the same sum for the same time and at the same rate?
  A.  Rs. 119
  B.  Rs. 129
  C.  Rs. 131
  D.  Rs. 139
Solution
B.G = S.I on T.D =Rs.(120x15x1/2x1/100)
= Rs.9.
(B.D)- (T.D) =Rs.9
B.D
= Rs.(120 + 9)
=Rs.129.
4. The banker's discount of a certain sum of money is Rs.72 and the true discount on the same sum for the same time is Rs.60. The sum due is
  A.  Rs. 360
  B.  Rs. 432
  C.  Rs. 540
  D.  Rs.1080
Solution
Sum Given, T.D =60, B.D = 72
= (B.D x T.D / B. D - T.D)
= Rs.(72x60/72-60)
= Rs.(72 x 60 / 12)
= Rs.(4320/ 12)
= Rs. 360.
5. The true discount on a bill of Rs.540 is Rs.90.The banker's discount is
  A.  Rs.60
  B.  Rs.108
  C.  Rs.110
  D.  Rs.112
Solution
P.W = Rs.(540 - 90)
= Rs. 450
S.I on Rs. 540 =Rs.(90/450 x 540)
= Rs. 108.
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