If A can do a work in 5 days and B can do a same work in 6 days. if both work together find how many days they complete the work.?

Options

A. 25/11 days
B. 28/11 days
C. 30/11 days
D. 11/30 days

Answer

To solve the problem of how long A and B will take to complete the work together, we can follow these steps:

### Step 1: Determine the work rates of A and B
- A can complete the work in 5 days.
- B can complete the work in 6 days.

### Step 2: Calculate the work done by A and B in one day
- The work rate of A (work done by A in one day) = \( \frac{1}{5} \) (since A completes the work in 5 days).
- The work rate of B (work done by B in one day) = \( \frac{1}{6} \) (since B completes the work in 6 days).

### Step 3: Add the work rates of A and B
- Together, their combined work rate = \( \frac{1}{5} + \frac{1}{6} \).

### Step 4: Find a common denominator to add the fractions
- The least common multiple (LCM) of 5 and 6 is 30.
- Convert \( \frac{1}{5} \) and \( \frac{1}{6} \) to have a common denominator of 30:
- \( \frac{1}{5} = \frac{6}{30} \)
- \( \frac{1}{6} = \frac{5}{30} \)

### Step 5: Add the fractions
- Now add the two fractions:
\[ \frac{6}{30} + \frac{5}{30} = \frac{11}{30} \]

### Step 6: Calculate the time taken to complete the work together
- The combined work rate \( \frac{11}{30} \) means that together, A and B can complete \( \frac{11}{30} \) of the work in one day.
- To find out how many days they will take to complete the entire work, take the reciprocal of their combined work rate:
\[ \text{Time taken} = \frac{30}{11} \text{ days} \]

### Conclusion
- Therefore, A and B together will complete the work in \( \frac{30}{11} \) days.

### Final Answer
- The answer is \( \frac{30}{11} \) days or approximately 2.73 days.

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