Discussion
A sum becomes Rs. 3000 at the rate of 12% per annum (simple interest). The same sum becomes Rs. 3300 at the rate of 15% per annum (simple interest) in the same duration. Find the sum and the duration.
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Write both amounts for the same \( P \) and \( T \).
\[ P + \frac{12PT}{100} = 3000, \qquad P + \frac{15PT}{100} = 3300 \]
Subtracting:
\[ \frac{3PT}{100} = 300 \quad\Longrightarrow\quad PT = 10{,}000 \]
Substituting back:
\[ P + 0.12 \times 10000 = 3000 \quad\Longrightarrow\quad P = \text{Rs. } 1800 \]
\[ T = \frac{10000}{1800} = 5.56 \approx 5.5 \text{ years} \]
Subtracting the two equations removes the principal and leaves the product \( PT \) - the key step.
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