Discussion
The present worth of a bill due some time hence is ₹1,500 and the true discount is ₹30. What is the banker’s discount?
Answer: B
Correct answer: ₹30.60
The banker’s gain is the simple interest on the true discount, which gives the standard relation \[ \text{BG} = \frac{\text{TD}^{2}}{\text{PW}}. \] Substituting, \[ \text{BG} = \frac{30^{2}}{1500} = \frac{900}{1500} = 0.60. \] The banker’s discount then follows from \( \text{BD} = \text{TD} + \text{BG} \): \[ \text{BD} = 30 + 0.60 = 30.60. \] The relationships worth holding together are these. True discount is the interest on the present worth; banker’s discount is the interest on the face value, which is larger; and the banker’s gain is the difference between them, which is why BD always exceeds TD. The trap is to treat BD as equal to TD, which the small size of BG makes tempting on figures like these.
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