A sum of money Rs 1750 is divided in 2 parts such tha the simple interest rate 8% per annum on the first part and 6% per annum on the 2nd part is equal after 2 year. Then find the ratio of principal.

Options

A. `850 : 1000`
B. `700 : 1000`
C. `750: 1000`
D. `950 : 1000`

Answer

To solve the problem, we need to find the ratio of two parts of a sum of Rs 1750 that are invested at different simple interest rates, such that the interest earned from both parts is equal after 2 years.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the first part of the money be \( A \) and the second part be \( B \).
We know that:
\[ A + B = 1750 \]

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

For the first part (A) at 8% for 2 years:
\[ \text{SI}_1 = \frac{A \times 8 \times 2}{100} = \frac{16A}{100} = 0.16A \]

For the second part (B) at 6% for 2 years:
\[ \text{SI}_2 = \frac{B \times 6 \times 2}{100} = \frac{12B}{100} = 0.12B \]

3. **Set the Simple Interests Equal:**
According to the problem, the simple interests are equal:
\[ 0.16A = 0.12B \]

4. **Rearrange the Equation:**
Rearranging gives us:
\[ \frac{A}{B} = \frac{0.12}{0.16} = \frac{12}{16} = \frac{3}{4} \]

5. **Express A and B in Terms of a Common Variable:**
Let \( A = 3x \) and \( B = 4x \) for some \( x \).

6. **Substitute Back into the Total:**
Substitute \( A \) and \( B \) back into the total:
\[ 3x + 4x = 1750 \implies 7x = 1750 \]

7. **Solve for x:**
\[ x = \frac{1750}{7} = 250 \]

8. **Find A and B:**
Now substitute back to find \( A \) and \( B \):
\[ A = 3x = 3 \times 250 = 750 \]
\[ B = 4x = 4 \times 250 = 1000 \]

9. **Find the Ratio:**
The ratio of \( A \) to \( B \) is:
\[ A : B = 750 : 1000 = 3 : 4 \]

### Final Answer:
The ratio of the principal amounts is \( 3 : 4 \).