Discussion
The banker’s gain on a sum due 4 years hence at 5% per annum is ₹20. What is the banker’s discount?
Answer: A
Correct answer: ₹120
Two steps are needed. First, the banker’s gain is the simple interest on the true discount: \[ 20 = \frac{\text{TD} \times 5 \times 4}{100} = 0.2\,\text{TD} \;\Rightarrow\; \text{TD} = 100. \] Then \[ \text{BD} = \text{TD} + \text{BG} = 100 + 20 = 120. \] The distractor 100 is the true discount, offered for a reader who stops after the first step - which is the usual error on this pattern. The rest of the picture follows: the present worth is \( \text{TD}^{2}/\text{BG} = 10000/20 = 500 \), and the face value is 600. Note the geometric progression 500, 100, 20, each a fifth of the last, the ratio being \( RT/100 = 0.2 \). The order of size is always \( \text{PW} > \text{TD} > \text{BG} \) when \( RT < 100 \), which is a quick check on any answer.
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