The efficiencies of A, B and C are in the ratio 5: 3: 8. Working together they can complete a work in 30 days. A and B worked together for 20 days. The remaining work will be completed by C alone in:

Options

A. 30 days
B. 32 days
C. 36 days
D. 40 days

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the efficiencies of A, B, and C
Let the efficiencies of A, B, and C be represented as:
- Efficiency of A = 5K
- Efficiency of B = 3K
- Efficiency of C = 8K

### Step 2: Calculate the total efficiency
The total efficiency when A, B, and C work together is:
\[ \text{Total Efficiency} = 5K + 3K + 8K = 16K \]

### Step 3: Calculate the total work
Since A, B, and C can complete the work together in 30 days, the total work can be calculated as:
\[ \text{Total Work} = \text{Total Efficiency} \times \text{Time} = 16K \times 30 = 480K \text{ units} \]

### Step 4: Calculate the work done by A and B in 20 days
The combined efficiency of A and B is:
\[ \text{Efficiency of A and B} = 5K + 3K = 8K \]
The work done by A and B in 20 days is:
\[ \text{Work Done by A and B} = \text{Efficiency of A and B} \times \text{Time} = 8K \times 20 = 160K \text{ units} \]

### Step 5: Calculate the remaining work
The remaining work after A and B have worked for 20 days is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done by A and B} = 480K - 160K = 320K \text{ units} \]

### Step 6: Calculate the time taken by C to complete the remaining work
C's efficiency is 8K. The time taken by C to complete the remaining work is:
\[ \text{Time Taken by C} = \frac{\text{Remaining Work}}{\text{Efficiency of C}} = \frac{320K}{8K} = 40 \text{ days} \]

### Final Answer
C will complete the remaining work in **40 days**.

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