If C alone can complete two-third part of a work in 12 days, then in how many days C can complete the whole work?

Options

A. 24 days
B. 15 days
C. 8 days
D. 18 days

Answer

To solve the problem step by step, we will use the information given about C's work rate.

### Step 1: Understand the given information
C can complete two-thirds (2/3) of the work in 12 days.

### Step 2: Determine the time taken to complete the whole work
We need to find out how many days C would take to complete the entire work (1 whole work).

### Step 3: Use the formula for work completion
The formula to find the time taken to complete the whole work when a person can complete a fraction of the work in a certain number of days is:

\[ \text{Total time} = \text{Days taken} \times \frac{\text{Total work}}{\text{Part of work completed}} \]

In this case:
- Days taken = 12 days
- Part of work completed = 2/3
- Total work = 1 (whole work)

### Step 4: Substitute the values into the formula
We can substitute the values into the formula:

\[ \text{Total time} = 12 \times \frac{1}{\frac{2}{3}} \]

### Step 5: Simplify the expression
To simplify \(\frac{1}{\frac{2}{3}}\), we can multiply by the reciprocal:

\[ \frac{1}{\frac{2}{3}} = \frac{3}{2} \]

Now substituting this back into the equation:

\[ \text{Total time} = 12 \times \frac{3}{2} \]

### Step 6: Calculate the total time
Now, we can calculate:

\[ 12 \times \frac{3}{2} = 12 \times 1.5 = 18 \text{ days} \]

### Final Answer
C can complete the whole work in **18 days**.

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