Discussion
The banker’s discount on a sum of money for 1 year 6 months is ₹558 and the true discount on the same sum for 2 years is ₹600. What is the rate per cent per annum?
Answer: C
Correct answer: 12%
Let the face value be \( A \) and the rate \( R \). The banker’s discount is interest on the face value, so for 1.5 years \[ \frac{A \times R \times 1.5}{100} = 558 \;\Rightarrow\; AR = 37200. \] The true discount for 2 years is \[ \frac{A \times R \times 2}{100 + 2R} = 600 \;\Rightarrow\; \frac{2 \times 37200}{100 + 2R} = 600. \] Solving, \[ 74400 = 600(100 + 2R) = 60000 + 1200R \;\Rightarrow\; 1200R = 14400 \;\Rightarrow\; R = 12. \] The rate is 12% per annum, and the face value follows as \( A = 37200/12 = 3100 \). The step that makes this tractable is treating \( AR \) as a single unknown, which the first equation supplies directly - the two quantities never need to be separated until the end.
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