The ratio of two numbers is 5 : 9 and their difference is 44. What will be the smaller number among both the numbers?

Options

A. 50
B. 65
C. 55
D. 70

Answer

To solve the problem, we will follow these steps:

1. **Define the Variables**: Let the two numbers be represented as \(5x\) and \(9x\), where \(x\) is a common multiplier.

2. **Set Up the Equation for the Difference**: According to the problem, the difference between the two numbers is given as 44. Therefore, we can write the equation:
\[ 9x - 5x = 44 \]

3. **Simplify the Equation**: Simplifying the left-hand side gives:
\[ 4x = 44 \]

4. **Solve for \(x\)**: To find the value of \(x\), divide both sides of the equation by 4:
\[ x = \frac{44}{4} = 11 \]

5. **Calculate the Two Numbers**: Now that we have \(x\), we can find the two numbers:
- The first number (smaller number) is:
\[ 5x = 5 \times 11 = 55 \]
- The second number (larger number) is:
\[ 9x = 9 \times 11 = 99 \]

6. **Identify the Smaller Number**: From the calculations, the smaller number is:
\[ \text{Smaller number} = 55 \]

Thus, the smaller number among both the numbers is **55**.