Discussion
The banker’s discount and the true discount on a sum due some time hence are ₹120 and ₹110 respectively. What is the sum due?
Answer: D
Correct answer: ₹1,320
The face value follows from \[ A = \frac{\text{BD} \times \text{TD}}{\text{BD} - \text{TD}}. \] The denominator is the banker’s gain, \( 120 - 110 = 10 \), so \[ A = \frac{120 \times 110}{10} = 1320. \] Checking against the definitions: the present worth is \( 1320 - 110 = 1210 \), and the ratio \( 110/1210 = 120/1320 \), both equal to \( 1/11 \) - confirming that the two discounts are computed at the same rate and time, with \( RT/100 = 1/11 \). The distractor 1,210 is that present worth, and 1,100 is a plausible-looking round figure with no basis; both are placed to catch a reader who stops one step early. Note also the geometric progression PW, TD, BG - here 1210, 110, 10 - each a tenth of the previous, which is a useful sanity check.
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