Discussion
If at same rate of interest, in 2 years, the simple interest is Rs. 40 and compound interest is Rs. 41, then what is the principal?
Answer: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Simple interest of Rs. 40 over two years means Rs. 20 each year. Compound interest exceeds it by Re. 1, and that excess is one year's interest on the first year's Rs. 20:
\[ 20 \times \frac{R}{100} = 1 \quad\Longrightarrow\quad R = 5\% \]
Now use the simple interest to find the principal:
\[ \frac{P \times 5 \times 2}{100} = 40 \quad\Longrightarrow\quad P = \text{Rs. } 400 \]
Reading the two-year gap as a rate directly is the standard shortcut for these, and it works because over two years the excess is always \( \text{SI}_{1} \times R \).
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