Discussion
If simple interest on a certain sum for 15 months at 7(1/2) % per annum exceeds the simple interest on the same sum for 8 months at 12(1/2)% per annum by Rs. 32.50, then the sum (in Rs.) is
Answer: C
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Convert both periods to years: 15 months is \( \tfrac{5}{4} \) and 8 months is \( \tfrac{2}{3} \).
\[ \frac{P \times 7.5 \times \tfrac{5}{4}}{100} - \frac{P \times 12.5 \times \tfrac{2}{3}}{100} = 32.50 \]
\[ \frac{P(9.375 - 8.3333)}{100} = 32.50 \]
\[ \frac{1.04167P}{100} = 32.50 \quad\Longrightarrow\quad P = \text{Rs. } 3120 \]
The two \( R \times T \) products are close (9.375 against 8.333), so the small difference needs a large principal to reach Rs. 32.50.
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