MAT Exam 2021 Paper

Concept:Simple interest is calculated using $\text{SI} = \frac{P \times R \times T}{100}$, where $R$ is the rate percent per annum and $T$ is the time in years.Explanation:Let the rate per cent per annum be $R$.According to the question, the number of years is equal to the rate, so $T = R$.Let the principal be $P$.Given that the simple interest is $\frac{1}{9}$ of the principal:$$\text{SI} = \frac{P}{9}$$Using the simple interest formula:$$\frac{P}{9} = \frac{P \times R \times T}{100}$$Since $T = R$, substitute $T = R$:$$\frac{P}{9} = \frac{P \times R \times R}{100}$$Cancel $P$ from both sides:$$\frac{1}{9} = \frac{R^2}{100}$$$$R^2 = \frac{100}{9}$$$$R = \sqrt{\frac{100}{9}} = \frac{10}{3} = 3.33$$Thus, the rate per cent per annum is $3.33\%$.Answer:$3.33\%$, i.e. Option C.