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Answer

ANSWER IS OPTION 2.

Answer

Sure! Here's a concise explanation:

### Problem Statement
- A and B can complete a work in 6 days.
- B and C can complete the same work in 9 days.
- B is twice as efficient as C.

### Solution
1. **Work Rates**:
   - \( B = 2C \)
   - \( A + 2C = \frac{1}{6} \)
   - \( 2C + C = \frac{1}{9} \implies C = \frac{1}{27} \)

2. **Calculate A**:
   - \( A + 2 \left( \frac{1}{27} \right) = \frac{1}{6} \implies A = \frac{7}{27} \)

3. **Combined Work Rate**:
   - \( A + B + C = \frac{7}{27} + \frac{2}{27} + \frac{1}{27} = \frac{10}{27} \)

4. **Time Taken**:
   - \( \frac{1}{\frac{10}{27}} = \frac{27}{10} = 2.7 \) days

So, A, B, and C together will take approximately \( 2.7 \) days to complete the work.

Answer

A and B can do a work in 6 days 

The number of days A and B combine to do the work = 1/6

A+B = 1/6

B and C can do a work in 9 days 

The number of days B and C combine to do the work = 1/9

B+C = 1/9

B is twice as efficient as C

B = 2C

2C+C  = 1/9

3C =1/9

C = 1/27

B = 2(1/27) = 2/27

A+B = 1/6

A = 1/6-B = 1/6-2/27 = (9-4)/54=5/54

A+B+C = 1/6+1/27 = (9+2)/54

= 11/54

The number of days take for A, B and C to complete the work = 54/11 = 4(10/11)

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