Discussion

Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?

Answer: D

Simple interest of Rs. 20 over two years is Rs. 10 a year. Compound interest exceeds it by Re. 1, which is one year's interest on that first Rs. 10:

\[ 10 \times \frac{R}{100} = 1 \quad\Longrightarrow\quad R = 10\% \]

Now use the simple interest to find the principal:

\[ 20 = \frac{P \times 10 \times 2}{100} = 0.2P \quad\Longrightarrow\quad P = \text{Rs. } 100 \]

Checking: at 10%, Rs. 100 gives compound interest of \( 100(1.21 - 1) = 21 \).

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