Sum of two numbers is 21 and their difference is 11, then the greatest number is

Options

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

Answer

To solve the problem step by step, we will define the two numbers and set up equations based on the information given in the question.

### Step 1: Define the variables
Let the two numbers be \( X \) and \( Y \).

### Step 2: Set up the equations
According to the problem:
1. The sum of the two numbers is 21:
\[ X + Y = 21 \quad \text{(Equation 1)} \]
2. The difference between the two numbers is 11:
\[ X - Y = 11 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
To find the values of \( X \) and \( Y \), we can add Equation 1 and Equation 2 together.

Adding the two equations:
\[ (X + Y) + (X - Y) = 21 + 11 \]
This simplifies to:
\[ 2X = 32 \]

### Step 4: Solve for \( X \)
Now, divide both sides by 2:
\[ X = \frac{32}{2} = 16 \]

### Step 5: 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 6: Identify the greatest number
Now we have both numbers:
- \( X = 16 \)
- \( Y = 5 \)

The greatest number is \( X \), which is:
\[ \text{Greatest number} = 16 \]

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

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