A man invests Rs 9000 at simple interest for 2 years at 3R% per annum. If the total interest received is Rs 5400, find the value of R.

The correct answer is 10%.

Step-by-step Explanation:

We are given the following values from the problem statement:

Principal ($P$) = Rs 9000

Time period ($T$) = 2 years

Rate of interest ($r$) = 3R% per annum

Simple Interest ($\mathrm{SI}$) = Rs 5400

Formula:

The formula for simple interest is given by:

$\mathrm{SI}=\frac{P\times r\times T}{100}$

Step 1: Substitute the given values into the formula.

$5400=\frac{9000\times \mathrm{3R}\times 2}{100}$

Step 2: Simplify the equation.

Canceling out the zeros in the numerator and denominator on the right side:

$5400=90\times \mathrm{3R}\times 2$

$5400=540\times R$

Step 3: Solve for R.

$R=\frac{5400}{540}$

$R=10$

Therefore, the value of R is 10, which corresponds to 10%.