Discussion
The banker’s discount on ₹2,200 at 12% per annum is the same as the true discount on ₹2,420 for the same time and rate. What is the time?
Answer: B
Correct answer: 10 months
Write both discounts in terms of the time \( T \) in years. The banker’s discount is simple interest on the face value: \[ \text{BD} = \frac{2200 \times 12 \times T}{100} = 264T. \] The true discount is \[ \text{TD} = \frac{2420 \times 12 \times T}{100 + 12T} = \frac{29040T}{100 + 12T}. \] Setting them equal and cancelling \( T \), \[ 264(100 + 12T) = 29040 \;\Rightarrow\; 26400 + 3168T = 29040 \;\Rightarrow\; T = \frac{2640}{3168} = \frac{5}{6}\text{ year}, \] which is 10 months. The step that matters is remembering that TD is calculated on the present worth, which is why its denominator carries the \( 100 + RT \) rather than 100.
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