Discussion
The banker’s gain on a bill is ₹12 and the true discount is ₹120. What is the banker’s discount?
Answer: A
Correct answer: ₹132
The three quantities are related by \[ \text{BD} = \text{TD} + \text{BG} = 120 + 12 = 132. \] The relation holds because the banker’s discount is simple interest on the face value while the true discount is simple interest on the present worth. Since the face value exceeds the present worth by exactly the true discount, the extra interest is the interest on TD - which is precisely what the banker’s gain is. From \( \text{BG} = \text{TD}^{2}/\text{PW} \), the present worth here is \( 120^{2}/12 = 1200 \), and the face value is \( 1200 + 120 = 1320 \). Note the geometric progression 1200, 120, 12 - each a tenth of the previous, the ratio being \( RT/100 = 0.1 \). The banker’s discount always exceeds the true discount, so 108 can be rejected on sight.
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