Questions & Answers: "Unitary Method and Simple Interest"

Let P be the principal and R be the rate of interest per annum.The amount (A) with simple interest is given by $A = P + \frac{P \times R \times T}{100}$.Given:Amount after 5 years ($A_5$) = Rs. 10800$P + \frac{P \times R \times 5}{100} = 10800 \quad (1)$Amount after 3 years ($A_3$) = Rs. 9680$P + \frac{P \times R \times 3}{100} = 9680 \quad (2)$Subtract equation (2) from equation (1):$\left(P + \frac{5PR}{100}\right) - \left(P + \frac{3PR}{100}\right) = 10800 - 9680$ $\frac{2PR}{100} = 1120$ This means the simple interest for 2 years is Rs. 1120.So, the simple interest for 1 year ($SI_1$) is $\frac{1120}{2} = 560$ Rs. Now, we can find the simple interest for 3 years ($SI_3$):$SI_3 = 3 \times SI_1 = 3 \times 560 = 1680\text{ Rs.}$Using equation (2), $A_3 = P + SI_3$:$9680 = P + 1680$ $P = 9680 - 1680$ $P = 8000\text{ Rs.}$ Now, we can find the rate of interest (R) using $SI_1 = \frac{P \times R \times 1}{100}$:$560 = \frac{8000 \times R \times 1}{100}$ $560 = 80R$ $R = \frac{560}{80}$ $R = 7\%$ Thus, the principal is Rs. 8000 and the rate of interest is 7%.