There is a number consisting of two digits, the digit in the units place is twice that in the tens' place and if 2 be subtracted from the sum of the digits, the difference is equal to `(1)/(6)` th of the number. The number is

Options

A. 26
B. 25
C. 24
D. 23

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define the digits
Let:
- \( x \) = digit in the tens place
- \( y \) = digit in the units place

### Step 2: Establish the relationship between the digits
According to the problem, the digit in the units place is twice that in the tens place. Therefore, we can express this relationship as:
\[ y = 2x \]

### Step 3: Express the number
The two-digit number can be expressed as:
\[ \text{Number} = 10x + y \]

### Step 4: Substitute \( y \) in the number expression
Substituting \( y \) from Step 2 into the number expression gives:
\[ \text{Number} = 10x + 2x = 12x \]

### Step 5: Set up the equation based on the sum of the digits
The sum of the digits is:
\[ x + y = x + 2x = 3x \]
According to the problem, if we subtract 2 from the sum of the digits, the result is equal to \( \frac{1}{6} \) of the number. This can be expressed as:
\[ 3x - 2 = \frac{1}{6}(12x) \]

### Step 6: Simplify the equation
Now, simplify the right side:
\[ 3x - 2 = 2x \]

### Step 7: Solve for \( x \)
Rearranging the equation gives:
\[ 3x - 2x = 2 \]
\[ x = 2 \]

### Step 8: Find \( y \)
Now substitute \( x \) back into the equation for \( y \):
\[ y = 2x = 2(2) = 4 \]

### Step 9: Determine the number
Now we can find the original two-digit number:
\[ \text{Number} = 10x + y = 10(2) + 4 = 20 + 4 = 24 \]

### Final Answer
The number is \( 24 \).

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