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

Options

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

Answer

To find the greater number given that the sum and difference of two numbers are 21 and 11 respectively, we can follow these steps:

### Step 1: Set up the equations
Let the two numbers be \( x \) and \( y \). According to the problem, we have:
1. \( x + y = 21 \) (Equation 1)
2. \( x - y = 11 \) (Equation 2)

### Step 2: Solve the equations
We can solve these two equations simultaneously.

**Add Equation 1 and Equation 2:**
\[ (x + y) + (x - y) = 21 + 11 \]
This simplifies to:
\[ 2x = 32 \]
Now, divide both sides by 2:
\[ x = 16 \]

### Step 3: Find the value of \( y \)
Now that we have \( x \), we can substitute \( x \) back into Equation 1 to find \( y \):
\[ 16 + y = 21 \]
Subtract 16 from both sides:
\[ y = 21 - 16 = 5 \]

### Step 4: Identify the greater number
Now we have both numbers:
- \( x = 16 \)
- \( y = 5 \)

The greater number is \( 16 \).

### Final Answer
The greater number is **16**.

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