A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been

Options

A. 124
B. 122
C. 118
D. 114

Answer

To solve the problem step by step, let's denote the unknown number as \( X \).

### Step 1: Understand the incorrect operation
The student first added 12 to the number \( X \) and then divided the result by 6. According to the problem, this operation resulted in 112:
\[ \frac{X + 12}{6} = 112 \]

### Step 2: Solve for \( X \)
To find \( X \), we will first multiply both sides of the equation by 6 to eliminate the fraction:
\[ X + 12 = 112 \times 6 \]
Calculating the right side:
\[ 112 \times 6 = 672 \]
So, we have:
\[ X + 12 = 672 \]

Next, we will subtract 12 from both sides to solve for \( X \):
\[ X = 672 - 12 \]
Calculating this gives:
\[ X = 660 \]

### Step 3: Perform the correct operation
Now, we need to perform the correct operation, which is to divide \( X \) by 6 and then add 12 to the quotient:
\[ \text{Correct Answer} = \frac{X}{6} + 12 \]
Substituting \( X = 660 \):
\[ \text{Correct Answer} = \frac{660}{6} + 12 \]

### Step 4: Calculate \( \frac{660}{6} \)
Calculating the division:
\[ \frac{660}{6} = 110 \]

### Step 5: Add 12 to the quotient
Now, we add 12 to the quotient:
\[ \text{Correct Answer} = 110 + 12 = 122 \]

### Final Answer
The correct answer should have been:
\[ \boxed{122} \]