A sum of money Rs 1,750 is divided in two parts such that the simple interest @ 8% per annum on first part and 6% per annum on 2nd part is equal after one year. Find the interest on each parts.

Options

A. Rs 150
B. Rs 60
C. Rs 100
D. Rs 80

Answer

To solve the problem, we need to find the two parts of the sum of money Rs 1,750 such that the simple interest on each part after one year is equal. Let's denote the first part as A and the second part as B.

### Step-by-Step Solution:

1. **Set Up the Equation for Simple Interest:**
The simple interest (SI) for the first part (A) at 8% for one year is:
\[ SI_1 = \frac{8}{100} \times A = 0.08A \]
The simple interest for the second part (B) at 6% for one year is:
\[ SI_2 = \frac{6}{100} \times B = 0.06B \]
According to the problem, these two interests are equal:
\[ 0.08A = 0.06B \]

2. **Express One Variable in Terms of the Other:**
Rearranging the equation gives:
\[ \frac{A}{B} = \frac{0.06}{0.08} = \frac{6}{8} = \frac{3}{4} \]
This means that A is to B as 3 is to 4. We can express A and B in terms of a common variable:
\[ A = 3x \quad \text{and} \quad B = 4x \]

3. **Use the Total Amount to Find x:**
According to the problem, the total amount is Rs 1,750:
\[ A + B = 1750 \]
Substituting the expressions for A and B:
\[ 3x + 4x = 1750 \]
\[ 7x = 1750 \]
Dividing both sides by 7:
\[ x = \frac{1750}{7} = 250 \]

4. **Find A and B:**
Now we can find the values of A and B:
\[ A = 3x = 3 \times 250 = 750 \]
\[ B = 4x = 4 \times 250 = 1000 \]

5. **Calculate the Simple Interest for Each Part:**
Now we can calculate the simple interest for each part:
- For A:
\[ SI_1 = 0.08 \times 750 = 60 \]
- For B:
\[ SI_2 = 0.06 \times 1000 = 60 \]

### Final Answer:
The interest on each part after one year is Rs 60.