The simple interest on ₹ 4,000 in 3 years at the rate of x% per annum equals the simple interest on ₹ 5,000 at the rate of 12% per annum in 2 years. The value of x is.

`x%` प्रति वर्ष की दर से `₹ 4,000` का 3 वर्ष का साधारण ब्याज, 12% प्रति वर्ष की दर से `₹ 5,000` पर 2 वर्ष के साधारण ब्याज के बराबर है, तो x का मान है-

Options

A. `10%`
B. `6%`
C. `8%`
D. `9%`

Explanation

To solve the problem, we need to find the value of \( x \) based on the information given about simple interest.

### Step 1: Calculate the Simple Interest on ₹ 5,000 at 12% per annum for 2 years.

The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For ₹ 5,000 at 12% for 2 years:
\[ SI = \frac{5000 \times 12 \times 2}{100} \]
\[ SI = \frac{5000 \times 24}{100} \]
\[ SI = \frac{120000}{100} = 1200 \]

### Step 2: Set up the equation for the Simple Interest on ₹ 4,000 at \( x\% \) for 3 years.

Using the same formula for Simple Interest:
For ₹ 4,000 at \( x\% \) for 3 years:
\[ SI = \frac{4000 \times x \times 3}{100} \]
\[ SI = \frac{12000x}{100} = 120x \]

### Step 3: Equate the two Simple Interest amounts.

From the problem statement, we know that the Simple Interest on ₹ 4,000 equals the Simple Interest on ₹ 5,000:
\[ 120x = 1200 \]

### Step 4: Solve for \( x \).

To find \( x \), divide both sides of the equation by 120:
\[ x = \frac{1200}{120} \]
\[ x = 10 \]

### Conclusion

The value of \( x \) is \( 10\% \).

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