What is the difference between the digits of a two digit number ?
(i) The sum of the digits of that number is 8
(ii) One-fifthe of that number is 15 less than half of 44.

Answer

To find the difference between the digits of a two-digit number based on the given conditions, we can follow these steps:

### Step 1: Define the two-digit number
Let the two-digit number be represented as \( XY \), where \( X \) is the tens digit and \( Y \) is the units digit.

### Step 2: Set up the equations based on the conditions
From the first condition, we know:
1. The sum of the digits is 8:
\[ X + Y = 8 \]

From the second condition, we know:
2. One-fifth of the number is 15 less than half of 44:
\[ \frac{XY}{5} = \frac{44}{2} - 15 \]
Simplifying the right side:
\[ \frac{44}{2} = 22 \quad \text{so} \quad 22 - 15 = 7 \]
Therefore, we have:
\[ \frac{XY}{5} = 7 \]

### Step 3: Solve for the two-digit number
To find \( XY \), we multiply both sides of the equation by 5:
\[ XY = 7 \times 5 = 35 \]

### Step 4: Identify the digits
Now, we can identify the digits of the number 35:
- \( X = 3 \) (tens digit)
- \( Y = 5 \) (units digit)

### Step 5: Calculate the difference between the digits
The difference between the digits \( X \) and \( Y \) is:
\[ |X - Y| = |3 - 5| = 2 \]

### Final Answer
The difference between the digits of the two-digit number is **2**.

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