When a two digit number is reversed, then the new number becomes `5/6 th` of the original number. The two digits differs by one.The original number is :

Options

A. 56
B. 45
C. 48
D. 54

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the two-digit number
Let the two-digit number be represented as \(10a + b\), where \(a\) is the tens digit and \(b\) is the units digit.

### Step 2: Set up the relationship for the reversed number
When the number is reversed, it becomes \(10b + a\). According to the problem, this reversed number is \( \frac{5}{6} \) of the original number. Therefore, we can write the equation:
\[ 10b + a = \frac{5}{6}(10a + b) \]

### Step 3: Clear the fraction
To eliminate the fraction, multiply both sides of the equation by 6:
\[ 6(10b + a) = 5(10a + b) \]
This simplifies to:
\[ 60b + 6a = 50a + 5b \]

### Step 4: Rearrange the equation
Now, rearranging the equation gives:
\[ 60b - 5b = 50a - 6a \]
\[ 55b = 44a \]
Dividing both sides by 11 results in:
\[ 5b = 4a \]

### Step 5: Express one variable in terms of the other
From the equation \(5b = 4a\), we can express \(b\) in terms of \(a\):
\[ b = \frac{4}{5}a \]

### Step 6: Use the condition that the digits differ by one
We know from the problem that the two digits differ by one:
\[ |a - b| = 1 \]
Substituting \(b = \frac{4}{5}a\) into this condition gives:
\[ |a - \frac{4}{5}a| = 1 \]
This simplifies to:
\[ |\frac{1}{5}a| = 1 \]
Thus, we have:
\[ \frac{1}{5}a = 1 \quad \text{or} \quad \frac{1}{5}a = -1 \]
Since \(a\) is a digit (0-9), we only consider \( \frac{1}{5}a = 1 \):
\[ a = 5 \]

### Step 7: Find the value of \(b\)
Now substituting \(a = 5\) back into the equation for \(b\):
\[ b = \frac{4}{5} \cdot 5 = 4 \]

### Step 8: Form the original number
The original two-digit number is:
\[ 10a + b = 10 \cdot 5 + 4 = 54 \]

### Conclusion
Thus, the original number is **54**.

---