Question
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Answer: Option A
$$\eqalign{
& T.D. = \frac{{B.D. \times 100}}{{100 + \left( {R \times T} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left[ {\frac{{420 \times 100}}{{100 + \left( {15 \times \frac{1}{3}} \right)}}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{420 \times 100}}{{105}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,400 \cr} $$
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$$\eqalign{
& T.D. = \frac{{B.D. \times 100}}{{100 + \left( {R \times T} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left[ {\frac{{420 \times 100}}{{100 + \left( {15 \times \frac{1}{3}} \right)}}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{420 \times 100}}{{105}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,400 \cr} $$
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