What value will come in place of the question mark (?) in each of the following questions ?
`1 1/3-1 1/6=?-1 1/12-1/24`

Options

A. `1 7/24`
B. `1 5/24`
C. `1 1/6`
D. `2 7/24`

Answer

To solve the equation \( 1 \frac{1}{3} - 1 \frac{1}{6} = ? - 1 \frac{1}{12} - \frac{1}{24} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert \( 1 \frac{1}{3} \), \( 1 \frac{1}{6} \), \( 1 \frac{1}{12} \) into improper fractions.

- \( 1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3} \)
- \( 1 \frac{1}{6} = \frac{6 \times 1 + 1}{6} = \frac{7}{6} \)
- \( 1 \frac{1}{12} = \frac{12 \times 1 + 1}{12} = \frac{13}{12} \)

Now, we can rewrite the equation as:
\[ \frac{4}{3} - \frac{7}{6} = ? - \frac{13}{12} - \frac{1}{24} \]

### Step 2: Find a Common Denominator
To perform the subtraction, we need a common denominator. The least common multiple (LCM) of 3, 6, 12, and 24 is 24.

Now, convert each fraction:
- \( \frac{4}{3} = \frac{4 \times 8}{3 \times 8} = \frac{32}{24} \)
- \( \frac{7}{6} = \frac{7 \times 4}{6 \times 4} = \frac{28}{24} \)
- \( \frac{13}{12} = \frac{13 \times 2}{12 \times 2} = \frac{26}{24} \)
- \( \frac{1}{24} = \frac{1}{24} \)

### Step 3: Substitute and Simplify
Now substitute these values back into the equation:
\[ \frac{32}{24} - \frac{28}{24} = ? - \frac{26}{24} - \frac{1}{24} \]

Calculate the left side:
\[ \frac{32 - 28}{24} = \frac{4}{24} = \frac{1}{6} \]

### Step 4: Combine the Right Side
Now simplify the right side:
\[ ? - \left(\frac{26 + 1}{24}\right) = ? - \frac{27}{24} \]

### Step 5: Set Up the Equation
Now we have:
\[ \frac{1}{6} = ? - \frac{27}{24} \]

### Step 6: Isolate the Question Mark
Add \( \frac{27}{24} \) to both sides:
\[ ? = \frac{1}{6} + \frac{27}{24} \]

### Step 7: Find a Common Denominator for the Right Side
The LCM of 6 and 24 is 24. Convert \( \frac{1}{6} \):
\[ \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \]

Now add:
\[ ? = \frac{4}{24} + \frac{27}{24} = \frac{31}{24} \]

### Step 8: Convert Back to Mixed Number
Convert \( \frac{31}{24} \) back to a mixed number:
\[ 31 \div 24 = 1 \quad \text{(whole part)} \]
Remainder is \( 31 - 24 = 7 \), so:
\[ \frac{31}{24} = 1 \frac{7}{24} \]

### Final Answer
Thus, the value that comes in place of the question mark is:
\[ \boxed{1 \frac{7}{24}} \]