two sums of money are proportional to 8 : 13. If the first sum be Rs.48, then the addition of two sums are

Options

A. Rs.128
B. Rs.120
C. Rs.124
D. Rs.126

Answer

To solve the problem, we need to find the total of two sums of money that are in the ratio of 8:13, given that the first sum is Rs. 48.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The two sums of money are in the ratio of 8:13. This means that if the first sum is represented as 8 parts, the second sum will be represented as 13 parts.

2. **Assign Values to the Parts**:
Let the first sum be \(8x\) and the second sum be \(13x\), where \(x\) is a common multiplier.

3. **Set Up the Equation**:
According to the problem, the first sum is Rs. 48. Therefore, we can set up the equation:
\[ 8x = 48 \]

4. **Solve for \(x\)**:
To find the value of \(x\), divide both sides of the equation by 8:
\[ x = \frac{48}{8} = 6 \]

5. **Find the Second Sum**:
Now that we have \(x\), we can find the second sum:
\[ 13x = 13 \times 6 = 78 \]

6. **Calculate the Total of Both Sums**:
Now, we can find the total of the two sums:
\[ \text{Total} = 8x + 13x = 21x \]
Substituting the value of \(x\):
\[ \text{Total} = 21 \times 6 = 126 \]

### Final Answer:
The addition of the two sums is Rs. 126.