A number of two digits has 3 for its unit's digit, and the sum of digits is `1/7` of the number itself, The number is

Options

A. 43
B. 53
C. 63
D. 73

Answer

To solve the problem, we need to find a two-digit number where the unit's digit is 3, and the sum of the digits is \( \frac{1}{7} \) of the number itself.

Let's break this down step by step:

### Step 1: Define the digits
Let:
- \( X \) be the digit in the ten's place.
- \( Y \) be the digit in the unit's place.

Given that the unit's digit is 3, we have:
- \( Y = 3 \)

### Step 2: Write the two-digit number
The two-digit number can be expressed as:
\[ \text{Number} = 10X + Y = 10X + 3 \]

### Step 3: Set up the equation for the sum of the digits
The sum of the digits is:
\[ X + Y = X + 3 \]

According to the problem, this sum is equal to \( \frac{1}{7} \) of the number:
\[ X + 3 = \frac{1}{7}(10X + 3) \]

### Step 4: Clear the fraction
To eliminate the fraction, multiply both sides of the equation by 7:
\[ 7(X + 3) = 10X + 3 \]

### Step 5: Expand and simplify the equation
Expanding the left side:
\[ 7X + 21 = 10X + 3 \]

Now, rearranging the equation to isolate \( X \):
\[ 21 - 3 = 10X - 7X \]
\[ 18 = 3X \]

### Step 6: Solve for \( X \)
Dividing both sides by 3 gives:
\[ X = 6 \]

### Step 7: Find the two-digit number
Now that we have both digits:
- \( X = 6 \)
- \( Y = 3 \)

The two-digit number is:
\[ 10X + Y = 10(6) + 3 = 60 + 3 = 63 \]

### Conclusion
The two-digit number is **63**.

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