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 solve the problem of finding the greater number given the sum and difference of two numbers, we can follow these steps:

### Step 1: Define the Variables
Let the two numbers be \( x \) (the greater number) and \( y \) (the smaller number).

### Step 2: Set Up the Equations
From the problem, we know:
- The sum of the two numbers is 25:
\[ x + y = 25 \]
- The difference of the two numbers is 15:
\[ x - y = 15 \]

### Step 3: Solve the Equations
We can solve these two equations simultaneously. First, we can add both equations to eliminate \( y \):
\[ (x + y) + (x - y) = 25 + 15 \]
This simplifies to:
\[ 2x = 40 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 2:
\[ x = \frac{40}{2} = 20 \]

### Step 5: Solve for \( y \)
Now that we have \( x \), we can find \( y \) using the sum equation:
\[ x + y = 25 \]
Substituting \( x = 20 \):
\[ 20 + y = 25 \]
Now, solve for \( y \):
\[ y = 25 - 20 = 5 \]

### Step 6: Identify the Greater Number
Now we have both numbers:
- \( x = 20 \)
- \( y = 5 \)

The greater number is \( x \), which is **20**.

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

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