The simple interest on X 4000 in 3 yr at the rate of x% per annum equals to the simple interest on X 5000 at the rate of 12% per annum in 2 yr. The value of x is

Options

A. 0.06
B. 0.08
C. 0.09
D. 0.1

Answer

To solve the problem, we need to find the value of \( x \) such that the simple interest on \( 4000 \) at the rate of \( x\% \) per annum for \( 3 \) years is equal to the simple interest on \( 5000 \) at the rate of \( 12\% \) per annum for \( 2 \) years.

### Step-by-Step Solution:

1. **Write the formula for Simple Interest (SI)**:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Calculate the Simple Interest for the first case**:
- Principal \( P_1 = 4000 \)
- Rate \( R_1 = x \% \)
- Time \( T_1 = 3 \) years

Using the formula:
\[ \text{SI}_1 = \frac{4000 \times x \times 3}{100} = \frac{12000x}{100} = 120x \]

3. **Calculate the Simple Interest for the second case**:
- Principal \( P_2 = 5000 \)
- Rate \( R_2 = 12\% \)
- Time \( T_2 = 2 \) years

Using the formula:
\[ \text{SI}_2 = \frac{5000 \times 12 \times 2}{100} = \frac{120000}{100} = 1200 \]

4. **Set the two Simple Interests equal to each other**:
\[ 120x = 1200 \]

5. **Solve for \( x \)**:
- Divide both sides by \( 120 \):
\[ x = \frac{1200}{120} = 10 \]

6. **Conclusion**:
The value of \( x \) is \( 10\% \).