A two digit number exceeds 30 percent of another two digit number by 44. If the sum of these two difit number is 200, which of the following is the difference between these two digit numbers ?

Options

A. 32
B. 40
C. 16
D. Data Inadequate

Answer

To solve the problem step by step, we will define the two-digit numbers and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( X \) = the first two-digit number
- \( Y \) = the second two-digit number

### Step 2: Set Up the Equations
From the problem statement, we have two main pieces of information:
1. The sum of the two numbers is 200:
\[ X + Y = 200 \]
2. The first number exceeds 30% of the second number by 44:
\[ X = 0.3Y + 44 \]

### Step 3: Substitute and Rearrange
We can substitute the expression for \( X \) from the second equation into the first equation:
\[ 0.3Y + 44 + Y = 200 \]
Combine like terms:
\[ 1.3Y + 44 = 200 \]

### Step 4: Solve for \( Y \)
Now, isolate \( Y \):
\[ 1.3Y = 200 - 44 \]
\[ 1.3Y = 156 \]
\[ Y = \frac{156}{1.3} \]
Calculating \( Y \):
\[ Y = 120 \]

### Step 5: Find \( X \)
Now, substitute \( Y \) back into the equation for \( X \):
\[ X + 120 = 200 \]
\[ X = 200 - 120 \]
\[ X = 80 \]

### Step 6: Calculate the Difference
Now that we have both numbers:
- \( X = 80 \)
- \( Y = 120 \)

The difference between the two numbers is:
\[ |X - Y| = |80 - 120| = 40 \]

### Conclusion
The difference between the two-digit numbers is **40**.