Amulya does a piece of work in 2 days and Bindu does it in 6 days. In how many days will the two do it together?

Options

A. `2//3` days
B. `3//2` days
C. `5//3` days
D. 3 days

Answer

To solve the problem of how many days Amulya and Bindu will take to complete the work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- Amulya completes the work in 2 days, so in one day, she completes \( \frac{1}{2} \) of the work.
- Bindu completes the work in 6 days, so in one day, she completes \( \frac{1}{6} \) of the work.

### Step 2: Calculate the combined work done by both in one day.
- To find the total work done by both Amulya and Bindu together in one day, we add their individual contributions:
\[ \text{Work done together in one day} = \frac{1}{2} + \frac{1}{6} \]

### Step 3: Find a common denominator and add the fractions.
- The least common multiple of 2 and 6 is 6. We convert \( \frac{1}{2} \) to have a denominator of 6:
\[ \frac{1}{2} = \frac{3}{6} \]
- Now we can add the fractions:
\[ \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \]

### Step 4: Determine how many days they will take to complete the work together.
- If together they complete \( \frac{2}{3} \) of the work in one day, then to complete the entire work (1 whole), we can set up the equation:
\[ \text{Days} = \frac{1 \text{ work}}{\frac{2}{3} \text{ work/day}} = \frac{1 \times 3}{2} = \frac{3}{2} \text{ days} \]

### Conclusion:
- Therefore, Amulya and Bindu together will complete the work in \( \frac{3}{2} \) days, which is equivalent to 1.5 days.