The ratio of two numbers is `3:1` and their sum is 72. Find the difference the numbers.
A. 18
B. 36
C. 48
D. 54

Options

A. A
B. C
C. B
D. D

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the ratio
The ratio of the two numbers is given as `3:1`. This means that if we let the first number be `3x`, then the second number will be `x`.

### Step 2: Set up the equation for their sum
According to the problem, the sum of the two numbers is `72`. Therefore, we can write the equation:
\[ 3x + x = 72 \]

### Step 3: Simplify the equation
Combine the terms on the left side:
\[ 4x = 72 \]

### Step 4: Solve for x
To find the value of `x`, divide both sides of the equation by `4`:
\[ x = \frac{72}{4} \]
\[ x = 18 \]

### Step 5: Find the two numbers
Now that we have the value of `x`, we can find the two numbers:
- First number: \( 3x = 3 \times 18 = 54 \)
- Second number: \( x = 18 \)

### Step 6: Calculate the difference between the numbers
Now, we need to find the difference between the two numbers:
\[ \text{Difference} = 3x - x = 2x \]
Substituting the value of `x`:
\[ \text{Difference} = 2 \times 18 = 36 \]

### Conclusion
The difference between the two numbers is `36`.

### Final Answer
Thus, the correct answer is **B. 36**.

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