Discussion
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Answer: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Recover the principal from the compound interest.
\[ 525 = P\left[(1.1)^{2} - 1\right] = 0.21P \quad\Longrightarrow\quad P = \text{Rs. } 2500 \]
Double the time is 4 years and half the rate is 5%:
\[ \text{SI} = \frac{2500 \times 5 \times 4}{100} = \text{Rs. } 500 \]
Doubling the time while halving the rate leaves simple interest unchanged, since \( Rn \) is the same - the answer would be identical for 2 years at 10%.
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