Discussion
A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Answer: C
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Equal interests over the same period give
\[ \frac{p_{1} \times 9 \times T}{100} = \frac{p_{2} \times 12 \times T}{100} \]
\[ 9\,p_{1} = 12\,p_{2} \quad\Longrightarrow\quad \frac{p_{1}}{p_{2}} = \frac{12}{9} = \frac{4}{3} \]
The sums are in the inverse ratio of the rates: the lower rate needs the larger capital to earn as much.
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