The ratio of the efficiencies of A, B, C is 7:5:4. Working togehter, they can finish a work in 35 days. A and B work together for 28 days. The remaining work will be completed (in days) by C alone.

Options

A. 56
B. 63
C. 49
D. 60

Answer

To solve the problem step by step, we will follow the given information about the efficiencies of A, B, and C, and how they work together.

### Step 1: Determine the total efficiency of A, B, and C
The efficiencies of A, B, and C are given in the ratio 7:5:4.

Let the efficiencies be:
- Efficiency of A = 7x
- Efficiency of B = 5x
- Efficiency of C = 4x

Total efficiency of A, B, and C together:
\[ \text{Total Efficiency} = 7x + 5x + 4x = 16x \]

### Step 2: Calculate the total work done
It is given that A, B, and C together can finish the work in 35 days.

Using the formula:
\[ \text{Total Work} = \text{Total Efficiency} \times \text{Time} \]
We can calculate the total work:
\[ \text{Total Work} = 16x \times 35 = 560x \]

### Step 3: Calculate the work done by A and B in 28 days
Now, A and B work together for 28 days. Their combined efficiency is:
\[ \text{Efficiency of A and B} = 7x + 5x = 12x \]

The work done by A and B in 28 days is:
\[ \text{Work done by A and B} = \text{Efficiency of A and B} \times \text{Time} \]
\[ \text{Work done} = 12x \times 28 = 336x \]

### Step 4: Calculate the remaining work
Now, we can find the remaining work after A and B have worked for 28 days:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done by A and B} \]
\[ \text{Remaining Work} = 560x - 336x = 224x \]

### Step 5: Calculate the time taken by C to complete the remaining work
C will complete the remaining work alone. The efficiency of C is 4x.

Using the formula for time:
\[ \text{Time} = \frac{\text{Work}}{\text{Efficiency}} \]
We can calculate the time taken by C:
\[ \text{Time taken by C} = \frac{224x}{4x} = 56 \text{ days} \]

### Final Answer
C will take **56 days** to complete the remaining work.

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