A and B finish a job in 12 days. While A,B and C can finish it in 8 days. C alone will finish the job in-

Options

A. 14 days
B. 16 days
C. 10 days
D. 24 days

Answer

To solve the problem step by step, we will first determine the work done by A, B, and C.

### Step 1: Determine the total work
Given that A and B can finish the job in 12 days, we can assume the total work to be a common multiple of the days taken by A and B, which is 24 units of work (LCM of 12 and 8).

### Step 2: Calculate the efficiency of A and B
The efficiency of A and B together can be calculated as:
\[ \text{Efficiency of A + B} = \frac{\text{Total Work}}{\text{Days taken by A + B}} = \frac{24}{12} = 2 \text{ units of work per day} \]

### Step 3: Calculate the efficiency of A, B, and C
The efficiency of A, B, and C together can be calculated as:
\[ \text{Efficiency of A + B + C} = \frac{\text{Total Work}}{\text{Days taken by A + B + C}} = \frac{24}{8} = 3 \text{ units of work per day} \]

### Step 4: Determine the efficiency of C
We know that:
\[ \text{Efficiency of A + B} + \text{Efficiency of C} = \text{Efficiency of A + B + C} \]
Substituting the values we found:
\[ 2 + \text{Efficiency of C} = 3 \]
Solving for the efficiency of C:
\[ \text{Efficiency of C} = 3 - 2 = 1 \text{ unit of work per day} \]

### Step 5: Calculate the time taken by C to finish the job alone
Now that we know the efficiency of C, we can find out how long it will take C to complete the job alone:
\[ \text{Time taken by C} = \frac{\text{Total Work}}{\text{Efficiency of C}} = \frac{24}{1} = 24 \text{ days} \]

### Final Answer
C alone will finish the job in **24 days**.

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