Discussion
The present worth of a bill due 2 years hence at 10% per annum is ₹1,600. What is the banker’s discount?
Answer: D
Correct answer: ₹384
Work outwards from the present worth. The true discount is the simple interest on it: \[ \text{TD} = \frac{1600 \times 10 \times 2}{100} = 320. \] The face value is therefore \( A = 1600 + 320 = 1920 \), and the banker’s discount is the simple interest on that: \[ \text{BD} = \frac{1920 \times 20}{100} = 384. \] The distractor 320 is the true discount, which is what a reader gets by stopping one step early - and it is the commonest wrong answer on this pattern. As a check, the banker’s gain is \( 384 - 320 = 64 \), and the interest on the true discount of 320 at 20% is indeed \( 320 \times 0.2 = 64 \). Note again the geometric progression: 1600, 320, 64.
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