Two numbers are in the ratio `8:3`. If the sum of the number is 143, find the smaller number.

Options

A. 104
B. 84
C. 39
D. 40

Answer

To find the smaller number when two numbers are in the ratio of 8:3 and their sum is 143, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the two numbers be represented as \( 8x \) and \( 3x \), where \( x \) is a common multiplier.

2. **Set Up the Equation**:
According to the problem, the sum of these two numbers is 143. Therefore, we can write the equation:
\[ 8x + 3x = 143 \]

3. **Combine Like Terms**:
Combine the terms on the left side:
\[ 11x = 143 \]

4. **Solve for \( x \)**:
To find the value of \( x \), divide both sides of the equation by 11:
\[ x = \frac{143}{11} \]
Performing the division:
\[ x = 13 \]

5. **Find the Smaller Number**:
Now that we have \( x \), we can find the smaller number, which is \( 3x \):
\[ 3x = 3 \times 13 = 39 \]

6. **Conclusion**:
The smaller number is \( 39 \).