Discussion
1/5 part of an amount was given at 3% simple interest, 1/3 part was given at 5% simple interest, 2/5 parts at 9% simple interest and remaining part at 11% simple interest. The total interest received was Rs.297. How much amount was originally given?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
The four parts must account for the whole, so the last fraction is
\[ 1 - \frac{1}{5} - \frac{1}{3} - \frac{2}{5} = \frac{15 - 3 - 5 - 6}{15} = \frac{1}{15} \]
Adding the four interests for one year:
\[ \frac{P}{100}\left(\frac{3}{5} + \frac{5}{3} + \frac{18}{5} + \frac{11}{15}\right) = 297 \]
\[ \frac{P}{100} \times \frac{9 + 25 + 54 + 11}{15} = \frac{P}{100} \times \frac{99}{15} = 297 \]
\[ P = \frac{297 \times 1500}{99} = \text{Rs. } 4500 \]
The three named fractions come to \( \tfrac{14}{15} \), so the unnamed remainder is \( \tfrac{1}{15} \) - easy to overlook.
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