Sum of two numbers is thrice their difference. Their ratio is

Options

A. `1:2`
B. `2:1`
C. `3:1`
D. `1:3`

Answer

To solve the problem, we need to find the ratio of two numbers given that their sum is thrice their difference. Let's denote the two numbers as \( x \) and \( y \).

### Step-by-Step Solution:

1. **Set Up the Equation**:
We know from the problem statement that the sum of the two numbers is thrice their difference. This can be expressed mathematically as:
\[ x + y = 3(x - y) \]

2. **Expand the Right Side**:
Now, let's expand the right side of the equation:
\[ x + y = 3x - 3y \]

3. **Rearrange the Equation**:
Next, we will rearrange the equation to group the \( x \) and \( y \) terms:
\[ x + y - 3x + 3y = 0 \]
Simplifying this gives:
\[ -2x + 4y = 0 \]

4. **Isolate \( x \)**:
Now, let's isolate \( x \):
\[ 2x = 4y \]
Dividing both sides by 2 gives:
\[ x = 2y \]

5. **Find the Ratio**:
Now, we can express the ratio of \( x \) to \( y \):
\[ \frac{x}{y} = \frac{2y}{y} = 2 \]
Therefore, the ratio of \( x \) to \( y \) is:
\[ x : y = 2 : 1 \]

### Final Answer:
The ratio of the two numbers is \( 2 : 1 \).