When 20 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number?

Options

A. 40
B. 44
C. 46
D. 48

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Set up the equation
According to the problem, when 20 is subtracted from the number, it becomes \( \frac{7}{12} \) of the number. This can be expressed as:
\[ x - 20 = \frac{7}{12}x \]

### Step 3: Rearrange the equation
To solve for \( x \), we need to isolate \( x \) on one side. First, we can move \( \frac{7}{12}x \) to the left side of the equation:
\[ x - \frac{7}{12}x = 20 \]

### Step 4: Combine like terms
Now, we can combine the terms on the left side. To do this, we can express \( x \) as \( \frac{12}{12}x \):
\[ \frac{12}{12}x - \frac{7}{12}x = 20 \]
\[ \frac{5}{12}x = 20 \]

### Step 5: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by the reciprocal of \( \frac{5}{12} \), which is \( \frac{12}{5} \):
\[ x = 20 \times \frac{12}{5} \]
\[ x = \frac{240}{5} \]
\[ x = 48 \]

### Step 6: Find the sum of the digits of \( x \)
Now that we have found \( x = 48 \), we can find the sum of its digits:
\[ 4 + 8 = 12 \]

### Final Answer
The sum of the digits of the number is \( 12 \).

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