Discussion
The banker’s gain on a certain sum due 2 years hence at 10% per annum is ₹100. What is the present worth?
Answer: C
Correct answer: ₹2,500
The banker’s gain is the simple interest on the true discount, so \[ \text{BG} = \frac{\text{TD} \times R \times T}{100} \;\Rightarrow\; 100 = \frac{\text{TD} \times 10 \times 2}{100} = 0.2\,\text{TD}, \] giving \( \text{TD} = 500 \). Now use \( \text{BG} = \dfrac{\text{TD}^{2}}{\text{PW}} \): \[ \text{PW} = \frac{\text{TD}^{2}}{\text{BG}} = \frac{500^{2}}{100} = \frac{250000}{100} = 2500. \] The answer can be checked directly: the true discount on a present worth of 2,500 at 10% for 2 years is \( 2500 \times 0.2 = 500 \), and the interest on that 500 is 100 - which is the banker’s gain as given. The two formulas for BG - interest on TD, and \( \text{TD}^{2}/\text{PW} \) - are the pair that solves most problems of this kind.
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