The ratio of the efficiencies of A, B and C to do a certain work is 7:3:5. Working together, they can complete the work in 21 days. A and C worked together for 5 days. The remaining work will be completed by B alone in :

Options

A. 54 days
B. 45 days
C. 60 days
D. 85 days

Answer

To solve the problem step by step, we will follow the outlined process to find out how long it will take for B to complete the remaining work after A and C have worked together for 5 days.

### Step 1: Determine the efficiencies of A, B, and C
The efficiencies of A, B, and C are given in the ratio 7:3:5. This means:
- Efficiency of A = 7x
- Efficiency of B = 3x
- Efficiency of C = 5x

### Step 2: Calculate the total efficiency when A, B, and C work together
To find the total efficiency when A, B, and C work together, we add their efficiencies:
\[ \text{Total Efficiency} = 7x + 3x + 5x = 15x \]

### Step 3: Calculate the total work
It is given that A, B, and C together can complete the work in 21 days. Therefore, the total work can be calculated as:
\[ \text{Total Work} = \text{Total Efficiency} \times \text{Number of Days} = 15x \times 21 = 315x \]

### Step 4: Determine the efficiency of A and C working together
Now, we need to find out how much work A and C can do together in one day:
\[ \text{Efficiency of A and C} = 7x + 5x = 12x \]

### Step 5: Calculate the work done by A and C in 5 days
If A and C work together for 5 days, the total work done by them is:
\[ \text{Work done by A and C} = \text{Efficiency of A and C} \times \text{Number of Days} = 12x \times 5 = 60x \]

### Step 6: Calculate the remaining work
Now, we can find out the remaining work after A and C have worked for 5 days:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done by A and C} = 315x - 60x = 255x \]

### Step 7: Determine how long B will take to complete the remaining work
B's efficiency is 3x. To find out how many days B will take to complete the remaining work, we use the formula:
\[ \text{Days taken by B} = \frac{\text{Remaining Work}}{\text{Efficiency of B}} = \frac{255x}{3x} = 85 \text{ days} \]

### Final Answer
B will take **85 days** to complete the remaining work.

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