A can do `(1)/(4)`th of a piece of work in one day. While B can do `(1)/(6)`th of the work in a day. In how many days can they do the same work, working together?

Options

A. `2(1)/(5)`
B. 2
C. `2(2)/(5)`
D. `(5)/(15)`

Explanation

To solve the problem, we need to find out how many days A and B can complete the work together. Let's break it down step by step.

### Step 1: Determine the work done by A and B in one day.
- A can do \( \frac{1}{4} \) of the work in one day.
- B can do \( \frac{1}{6} \) of the work in one day.

### Step 2: Find the combined work done by A and B in one day.
To find the total work done by A and B together in one day, we add their individual work rates:
\[ \text{Work done by A in one day} + \text{Work done by B in one day} = \frac{1}{4} + \frac{1}{6} \]

### Step 3: Find a common denominator.
The least common multiple (LCM) of 4 and 6 is 12. We can convert the fractions:
\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{1}{6} = \frac{2}{12} \]

### Step 4: Add the fractions.
Now, we can add the two fractions:
\[ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \]

### Step 5: Calculate the total time taken to complete the work.
Since A and B together can complete \( \frac{5}{12} \) of the work in one day, we need to find out how many days it will take to complete 1 unit of work:
\[ \text{Time taken} = \frac{1 \text{ unit of work}}{\frac{5}{12} \text{ unit of work per day}} = 1 \times \frac{12}{5} = \frac{12}{5} \text{ days} \]

### Final Answer:
Thus, A and B together can complete the work in \( \frac{12}{5} \) days, which is equal to 2.4 days.

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