Discussion
The true discount on a sum due 2 years hence at 5% per annum is ₹75. What is the banker’s discount?
Answer: A
Correct answer: ₹82.50
The banker’s gain is the simple interest on the true discount: \[ \text{BG} = \frac{75 \times 5 \times 2}{100} = \frac{750}{100} = 7.50. \] The banker’s discount follows: \[ \text{BD} = \text{TD} + \text{BG} = 75 + 7.50 = 82.50. \] The same answer comes from the ratio \( \text{BD} = \text{TD} \times \dfrac{100 + RT}{100} = 75 \times \dfrac{110}{100} = 82.50 \), which is quicker when the rate and time are given. For completeness, the present worth is \( \text{TD} \times 100/(RT) = 75 \times 100/10 = 750 \), and the face value is 825. Note the progression 750, 75, 7.50 - present worth, true discount and banker’s gain, each a tenth of the last because \( RT/100 = 0.1 \). Spotting it gives the answer without any formula at all.
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