Two numbers are in the ratio of `2 : 3`. If their sum is 125, find the numbers.

Options

A. 50, 75
B. 24, 36
C. 20. 30
D. 32, 78

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the numbers in terms of a variable
Let the two numbers be represented as \(2x\) and \(3x\). This is based on the given ratio of \(2:3\).

### Step 2: Write the equation for their sum
According to the problem, the sum of these two numbers is 125. Therefore, we can write the equation:
\[ 2x + 3x = 125 \]

### Step 3: Simplify the equation
Combine like terms on the left side of the equation:
\[ 5x = 125 \]

### Step 4: Solve for \(x\)
To find the value of \(x\), divide both sides of the equation by 5:
\[ x = \frac{125}{5} = 25 \]

### Step 5: Find the actual numbers
Now that we have \(x\), we can find the two numbers:
- The first number is \(2x = 2 \times 25 = 50\).
- The second number is \(3x = 3 \times 25 = 75\).

### Conclusion
The two numbers are \(50\) and \(75\).

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