Discussion
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Answer: B
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Equal interests give the ratio of the parts.
\[ \frac{p_{1} \times 3 \times 8}{100} = \frac{p_{2} \times 5 \times 3}{100} \]
\[ 24\,p_{1} = 15\,p_{2} \quad\Longrightarrow\quad \frac{p_{1}}{p_{2}} = \frac{15}{24} = \frac{5}{8} \]
So the sum splits into 13 shares of \( 2665 \div 13 = 205 \):
\[ p_{2} = 8 \times 205 = \text{Rs. } 1640 \]
The first part is Rs. 1025, and both yield Rs. 246 of interest.
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