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.

Answer: Option C

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
$$\begin{array}{rl}& =\text{Rs}\text{.}\left(6000\times 10\times \frac{1}{5}\times \frac{1}{100}\right)\\ & =\text{Rs}\text{.}120\\ & \text{T}\text{.D}\text{.}=\text{Rs}\text{.}\left[\frac{6000\times 10\times \frac{1}{5}}{100+\left(10\times \frac{1}{5}\right)}\right]\\ & =\text{Rs}\text{.}\frac{12000}{102}\\ & =\text{Rs}\text{.}117.64\end{array}$$
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