Discussion
The banker’s gain on a certain sum due 2 years hence at 5% per annum is ₹8. What is the true discount?
Answer: A
Correct answer: ₹80
The banker’s gain is the simple interest on the true discount: \[ \text{BG} = \frac{\text{TD} \times R \times T}{100}. \] Here \( R = 5 \) and \( T = 2 \), so \( RT = 10 \) and \[ 8 = \frac{\text{TD} \times 10}{100} = 0.1\,\text{TD} \;\Rightarrow\; \text{TD} = 80. \] The whole set follows from that. The present worth is \( \text{TD}^{2}/\text{BG} = 6400/8 = 800 \); the face value is \( 800 + 80 = 880 \); and the banker’s discount is \( 80 + 8 = 88 \). Note the geometric progression: PW, TD and BG stand as 800, 80, 8 - each a tenth of the previous, the ratio being \( RT/100 = 0.1 \). Recognising that pattern often gives the answer without any algebra at all. The distractor 88 is the banker’s discount, offered to catch the confusion between the two.
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