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 option is 10%.

Step-by-step Explanation:

1. Identify the given values from the problem:

• Principal amount ($P$) = Rs 9000

• Time period ($T$) = 2 years

• Rate of interest per annum = $3R\%$

• Total simple interest ($SI$) = Rs 5400

2. Use the Simple Interest formula:

The standard formula for calculating simple interest is:

$SI=\frac{P\×\text{Rate}\×T}{100}$

3. Substitute the values into the formula:

Here, the rate is $3R$.

$5400=\frac{9000\×3R\×2}{100}$

4. Simplify the equation to find the value of R:

Cancel out two zeros from 9000 and 100:

$5400=90\×3R\×2$

$5400=540R$

Now, divide both sides by 540:

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

$R=10$

Therefore, the value of $R$ is 10 (or 10%).