Two numbers are in the ratio `5:8`. If the sum of the number is `182`, find the numbers

Options

A. `70,112`
B. `80, 50`
C. `90, 110`
D. `100,82`

Answer

To solve the problem of finding two numbers in the ratio of 5:8, given that their sum is 182, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the two numbers be represented as \(5x\) and \(8x\), where \(x\) is a common multiplier.

2. **Set Up the Equation**:
According to the problem, the sum of these two numbers is equal to 182. Therefore, we can write the equation:
\[ 5x + 8x = 182 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 13x = 182 \]

4. **Solve for \(x\)**:
To find the value of \(x\), divide both sides of the equation by 13:
\[ x = \frac{182}{13} \]
Calculating this gives:
\[ x = 14 \]

5. **Find the Two Numbers**:
Now that we have the value of \(x\), we can find the two numbers:
- The first number is:
\[ 5x = 5 \times 14 = 70 \]
- The second number is:
\[ 8x = 8 \times 14 = 112 \]

6. **Conclusion**:
Therefore, the two numbers are 70 and 112.

### Final Answer:
The two numbers are **70** and **112**.

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