Q. The Compound interest of certain for first and Second year is Rs. 20 and Rs. 23 respectively. Find the rate of interest in P.C.P.A. Step 1: Identify the compound interest for the first year ($CI_1$) and the second year ($CI_2$). $$ CI_1 = \text{Rs. } 20 $$ $$ CI_2 = \text{Rs. } 23 $$ Step 2: Calculate the additional interest earned in the second year. This additional interest is the interest earned on the first year's interest. $$ \text{Additional Interest} = CI_2 - CI_1 = 23 - 20 = \text{Rs. } 3 $$ Step 3: Consider the first year's compound interest ($CI_1$) as the principal for calculating the additional interest. The time period for this additional interest is 1 year. Principal ($P$) = Rs. 20 Interest ($I$) = Rs. 3 Time ($T$) = 1 year Step 4: Use the simple interest formula $I = \frac{P \times R \times T}{100}$ to find the rate of interest ($R$). $$ 3 = \frac{20 \times R \times 1}{100} $$ Step 5: Solve for $R$. $$ 3 = \frac{20R}{100} $$ $$ 3 = \frac{R}{5} $$ Multiply both sides by 5: $$ R = 3 \times 5 $$ $$ R = 15 $$ The rate of interest is 15% per annum. The final answer is $\boxed{15\% \text{ P.C.P.A.}}$. That's 2 down. 3 left today — send the next one.