A is twice as efficient as B and B is thrice as efficient as C. Working together, they can finish a certain work in 5 days. If A and C worked together for 5 days then B alone would complete the remaining work in .......

Options

A. 8 days
B. 5 days
C. 6 days
D. 4 days

Answer

To solve the problem step by step, let's define the efficiencies of A, B, and C based on the information given.

### Step 1: Define the efficiencies
Let the efficiency of C be \( x \).
Then the efficiency of B, being thrice as efficient as C, is \( 3x \).
And the efficiency of A, being twice as efficient as B, is \( 2 \times 3x = 6x \).

### Step 2: Calculate total efficiency
Now, the total efficiency of A, B, and C working together is:
\[ \text{Efficiency of A} + \text{Efficiency of B} + \text{Efficiency of C} = 6x + 3x + x = 10x \]

### Step 3: Determine the work done in 5 days
According to the problem, A, B, and C can finish the work together in 5 days. Therefore, the total work (W) can be expressed as:
\[ W = \text{Total Efficiency} \times \text{Time} = 10x \times 5 = 50x \]

### Step 4: Work done by A and C in 5 days
Now, we need to find out how much work A and C can do together in 5 days. Their combined efficiency is:
\[ \text{Efficiency of A} + \text{Efficiency of C} = 6x + x = 7x \]
Thus, the work done by A and C in 5 days is:
\[ \text{Work done by A and C} = 7x \times 5 = 35x \]

### Step 5: Remaining work
The remaining work after A and C have worked for 5 days is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done by A and C} = 50x - 35x = 15x \]

### Step 6: Time taken by B to complete the remaining work
Now, we need to find out how long it will take for B to complete the remaining work. The efficiency of B is \( 3x \). The time taken by B to finish the remaining work is given by:
\[ \text{Time} = \frac{\text{Remaining Work}}{\text{Efficiency of B}} = \frac{15x}{3x} = 5 \text{ days} \]

### Final Answer
Thus, B alone would complete the remaining work in **5 days**.

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