Discussion
The banker’s discount on a sum due 2 years hence at 10% per annum is ₹60. What is the true discount?
Answer: B
Correct answer: ₹50
The two discounts are related by \[ \text{TD} = \frac{\text{BD} \times 100}{100 + RT}. \] Here \( RT = 10 \times 2 = 20 \), so \[ \text{TD} = \frac{60 \times 100}{120} = 50. \] The relation follows from what each discount is interest on. BD is interest on the face value \( A \); TD is interest on the present worth. Since \( A = \text{PW}\left(1 + \frac{RT}{100}\right) \), the two discounts stand in the ratio \( (100+RT) : 100 \). As a check, the banker’s gain is \( 60 - 50 = 10 \), and the interest on the true discount of 50 at 10% for 2 years is indeed \( 50 \times 0.2 = 10 \). The face value here is \( 60 \times 100/20 = 300 \) and the present worth 250.
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