Discussion
The true discount on a bill of ₹2,050 due 4 months hence is ₹50. What is the rate per cent per annum?
Answer: B
Correct answer: 15%
The present worth is \( 2050 - 50 = 2000 \), and the true discount is the simple interest on that: \[ 50 = \frac{2000 \times R \times \tfrac{1}{3}}{100} = \frac{2000R}{300}. \] Solving, \[ R = \frac{50 \times 300}{2000} = 7.5 \times 2 = 15. \] The rate is 15% per annum. The step that decides the problem is subtracting the discount first: the true discount is interest on the present worth, never on the face value. Using 2,050 instead gives \( R = 50 \times 300/2050 \approx 14.6\% \) - close enough to look right and wrong. Four months is \( \tfrac{1}{3} \) of a year, and converting the period to years before substituting is the other place errors creep in.
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