Discussion

The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?

Answer: D

The rate \( 6\tfrac{2}{3}\% \) is \( \tfrac{1}{15} \), so the yearly factor is \( \tfrac{16}{15} \). Over three years:

\[ \text{CI} - \text{SI} = P\left[\left(\frac{16}{15}\right)^{3} - 1 - \frac{3}{15}\right] \]

\[ \left(\frac{16}{15}\right)^{3} = \frac{4096}{3375} = 1.213629 \]

\[ 1.213629 - 1.2 = 0.013629 \]

\[ P = \frac{184}{0.013629} = \text{Rs. } 13{,}500 \]

Turning the awkward percentage into the fraction \( \tfrac{1}{15} \) first keeps the cube exact and avoids rounding drift.

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