A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.

Solution(By Examveda Team)

Face value of the bill = Rs. 6000
Date on which the bill was drawn = July 14 at 5 months
Nominally due date = December 14
Legally due date = December 17
Date on which the bill was discounted = October 5
Unexpired time :
Oct.   Nov.   Dec.
26   +   30   +   17 = 73 days = $$\frac{1}{5}$$ Years
B.D. = S.I. on Rs. 6000 for $$\frac{1}{5}$$ year
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left( {6000 \times 10 \times \frac{1}{5} \times \frac{1}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,120 \cr & {\text{T}}{\text{.D}}{\text{.}} = {\text{Rs}}{\text{.}}\,\left[ {\frac{{6000 \times 10 \times \frac{1}{5}}}{{100 + \left( {10 \times \frac{1}{5}} \right)}}} \right] \cr & = {\text{Rs}}{\text{.}}\,\frac{{12000}}{{102}} \cr & = {\text{Rs}}{\text{.}}\,117.64 \cr} $$
B.G. = B.D. - T.D. = Rs. 120 - 117.64 = Rs. 2.36
Money received by the holder of the bill = Rs. 6000 - 120 = Rs. 5880