Sum and difference of two numbers are 25 and 15 respectively. The greater number is

Options

A. 10
B. 15
C. 20
D. 25

Answer

To find the greater number given that the sum and difference of two numbers are 25 and 15 respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the two numbers be \( X \) and \( Y \).

2. **Set Up the Equations**:
From the problem, we know:
- The sum of the two numbers:
\[ X + Y = 25 \quad \text{(1)} \]
- The difference of the two numbers:
\[ X - Y = 15 \quad \text{(2)} \]

3. **Add the Two Equations**:
To eliminate \( Y \), we can add equations (1) and (2):
\[ (X + Y) + (X - Y) = 25 + 15 \]
Simplifying this gives:
\[ 2X = 40 \]

4. **Solve for \( X \)**:
Divide both sides by 2:
\[ X = \frac{40}{2} = 20 \]

5. **Substitute \( X \) Back to Find \( Y \)**:
Now that we have \( X \), we can substitute it back into equation (1) to find \( Y \):
\[ 20 + Y = 25 \]
Solving for \( Y \):
\[ Y = 25 - 20 = 5 \]

6. **Identify the Greater Number**:
Now we have both numbers:
- \( X = 20 \)
- \( Y = 5 \)
The greater number is \( 20 \).

### Final Answer:
The greater number is **20**.