Shailendra, Amit and Suraj can complete a work in 6, 12 and 15 days respectively. Find the time taken to complete the work if they are working together.

Options

A. 60/17 days
B. 60/23 days
C. 60/19 days
D. 60/29 days

Answer

To find the time taken to complete the work when Shailendra, Amit, and Suraj work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- Shailendra can complete the work in 6 days. Therefore, in one day, he completes:
\[ \text{Work done by Shailendra in one day} = \frac{1}{6} \text{ of the work} \]

- Amit can complete the work in 12 days. Therefore, in one day, he completes:
\[ \text{Work done by Amit in one day} = \frac{1}{12} \text{ of the work} \]

- Suraj can complete the work in 15 days. Therefore, in one day, he completes:
\[ \text{Work done by Suraj in one day} = \frac{1}{15} \text{ of the work} \]

### Step 2: Find the total work done by all three in one day.
- To find the total work done by all three in one day, we add their individual contributions:
\[ \text{Total work done in one day} = \frac{1}{6} + \frac{1}{12} + \frac{1}{15} \]

### Step 3: Calculate the LCM of the denominators.
- The denominators are 6, 12, and 15. The LCM of these numbers is 60.

### Step 4: Convert each fraction to have the same denominator.
- Convert each fraction:
\[ \frac{1}{6} = \frac{10}{60}, \quad \frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60} \]

### Step 5: Add the fractions.
- Now, we can add these fractions:
\[ \text{Total work done in one day} = \frac{10}{60} + \frac{5}{60} + \frac{4}{60} = \frac{19}{60} \]

### Step 6: Calculate the total time taken to complete the work.
- Since the total work is considered as 1 unit, the time taken to complete the work when all three work together is:
\[ \text{Time taken} = \frac{\text{Total work}}{\text{Total work done in one day}} = \frac{1}{\frac{19}{60}} = \frac{60}{19} \text{ days} \]

### Conclusion:
The time taken to complete the work when Shailendra, Amit, and Suraj work together is \(\frac{60}{19}\) days.

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