Discussion
The banker’s gain on a certain sum due 3 years hence at 8% per annum is ₹48. What is the banker’s discount?
Answer: C
Correct answer: ₹248
First find the true discount, since the banker’s gain is the simple interest on it: \[ 48 = \frac{\text{TD} \times 8 \times 3}{100} = 0.24\,\text{TD} \;\Rightarrow\; \text{TD} = \frac{4800}{24} = 200. \] Then \[ \text{BD} = \text{TD} + \text{BG} = 200 + 48 = 248. \] The distractor 200 is the true discount, which catches anyone who stops after the first step. For completeness, the present worth is \( \text{TD}^{2}/\text{BG} = 40000/48 \approx 833.33 \) and the face value about 1,033.33. The order of magnitude is always \( \text{PW} > \text{TD} > \text{BG} \) for ordinary rates, and BD lies just above TD - so any answer below the true discount can be rejected without arithmetic.
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