Discussion
A banker pays ₹2,910 on a bill of ₹3,000 discounted 4 months before it is due. What is the rate of discount per annum?
Answer: A
Correct answer: 9%
The banker’s discount is the amount deducted: \[ \text{BD} = 3000 - 2910 = 90. \] It is simple interest on the face value for the unexpired time, so \[ 90 = \frac{3000 \times R \times \tfrac{1}{3}}{100} = 10R \;\Rightarrow\; R = 9. \] The rate is 9% per annum. The point of the question is the phrase a banker pays: the sum handed over is the discounted value, and the difference from the face value is the banker’s discount rather than the true discount. Computing on the 2,910 instead would give \( R = 90 \times 300/2910 \approx 9.28\% \) - which would be the rate implied by the true discount, a different quantity. Four months must be converted to \( \tfrac{1}{3} \) of a year before substituting, which is where the other common slip occurs.
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