`16-:4=74`
`21-:7=33`
`81-:9=99`
then `55-:5=?`

Options

A. 110
B. 1001
C. 11
D. 1011

Explanation

To solve the problem step by step, we will first identify the pattern from the given equations and then apply it to the last equation.

### Step 1: Identify the Pattern
We have the following equations:
1. \( 16 \div 4 = 74 \)
2. \( 21 \div 7 = 33 \)
3. \( 81 \div 9 = 99 \)

Let's analyze the first equation:
- The first number is 16. The sum of its digits is \( 1 + 6 = 7 \).
- The second number is 4.
- If we divide 16 by 4, we get \( 16 \div 4 = 4 \).
- The result is written as 74, where 7 is the digit sum and 4 is the result of the division.

### Step 2: Apply the Same Logic to the Second Equation
For the second equation \( 21 \div 7 = 33 \):
- The sum of the digits of 21 is \( 2 + 1 = 3 \).
- Dividing 21 by 7 gives \( 21 \div 7 = 3 \).
- The result is written as 33, where 3 is the digit sum and 3 is the result of the division.

### Step 3: Apply the Same Logic to the Third Equation
For the third equation \( 81 \div 9 = 99 \):
- The sum of the digits of 81 is \( 8 + 1 = 9 \).
- Dividing 81 by 9 gives \( 81 \div 9 = 9 \).
- The result is written as 99, where 9 is the digit sum and 9 is the result of the division.

### Step 4: Solve for the Last Equation
Now, we need to solve \( 55 \div 5 = ? \):
- The sum of the digits of 55 is \( 5 + 5 = 10 \).
- Dividing 55 by 5 gives \( 55 \div 5 = 11 \).
- Therefore, we write the result as 101, where 10 is the digit sum and 11 is the result of the division.

### Final Answer
Thus, \( 55 \div 5 = 101 \).