Sum and differnce of two numbers are 21 and 11, respectively. Find the greater number.

Options

A. 5
B. 16
C. 9
D. 10

Answer

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

### Step 1: Set up the equations
We are given:
1. The sum of the two numbers:
\[ x + y = 21 \quad \text{(Equation 1)} \]
2. The difference of the two numbers:
\[ x - y = 11 \quad \text{(Equation 2)} \]

### Step 2: Add the two equations
To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 21 + 11 \]
This simplifies to:
\[ 2x = 32 \]

### Step 3: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{32}{2} = 16 \]

### Step 4: Substitute \( x \) back to find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 16 + y = 21 \]
Subtract 16 from both sides:
\[ y = 21 - 16 = 5 \]

### Step 5: Identify the greater number
Now we have both numbers:
- \( x = 16 \)
- \( y = 5 \)

The greater number is:
\[ \text{Greater number} = 16 \]

### Final Answer
The greater number is \( 16 \).

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