Discussion
Rs. 20400 was divided in two parts and then invested. One part invested at 6.25% for 8 years yields the same interest as the other part invested at 7% for 5 years. What is the value of smaller part?
Answer: B
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Equal interests give the ratio of the two parts.
\[ \frac{p_{1} \times 6.25 \times 8}{100} = \frac{p_{2} \times 7 \times 5}{100} \]
\[ 50\,p_{1} = 35\,p_{2} \quad\Longrightarrow\quad \frac{p_{1}}{p_{2}} = \frac{7}{10} \]
So the parts are 7 and 10 of 17 shares:
\[ p_{1} = \frac{7}{17} \times 20400 = \text{Rs. } 8400, \qquad p_{2} = \text{Rs. } 12{,}000 \]
The smaller part is Rs. 8400 - the one at the higher \( R \times T \) product, since it needs less capital for the same return.
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