Question
The banker's discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?
Answer: Option D
$$\eqalign{
& T = 6{\text{ months}} = \frac{1}{2}{\text{year}} \cr
& R = 6\% \cr
& TD = \frac{{BD \times 100}}{{100 + TR}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{100 + \left( {\frac{1}{2} \times 6} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{103}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{1854}}{{103}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,18 \cr} $$
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$$\eqalign{
& T = 6{\text{ months}} = \frac{1}{2}{\text{year}} \cr
& R = 6\% \cr
& TD = \frac{{BD \times 100}}{{100 + TR}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{100 + \left( {\frac{1}{2} \times 6} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{103}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{1854}}{{103}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,18 \cr} $$
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