If A, B, and C can do a piece of work in 15, 30, and 60 days respectively. In how many days together they will do the same work?

Options

A. 10 days
B. 12 days
C. 60/11 days
D. 60/7 days

Answer

To solve the problem, we need to find out how many days A, B, and C will take to complete the work together. Here’s a step-by-step solution:

### Step 1: Determine the work done by each person in one day.
- **A** can complete the work in 15 days. Therefore, A's work in one day is:
\[ \text{Work by A in one day} = \frac{1}{15} \]

- **B** can complete the work in 30 days. Therefore, B's work in one day is:
\[ \text{Work by B in one day} = \frac{1}{30} \]

- **C** can complete the work in 60 days. Therefore, C's work in one day is:
\[ \text{Work by C in one day} = \frac{1}{60} \]

### Step 2: Find the total work done by A, B, and C in one day.
To find the total work done by A, B, and C together in one day, we add their individual work rates:
\[ \text{Total work in one day} = \frac{1}{15} + \frac{1}{30} + \frac{1}{60} \]

### Step 3: Find a common denominator and add the fractions.
The least common multiple (LCM) of 15, 30, and 60 is 60. We convert each fraction:
\[ \frac{1}{15} = \frac{4}{60}, \quad \frac{1}{30} = \frac{2}{60}, \quad \frac{1}{60} = \frac{1}{60} \]
Now, adding these fractions:
\[ \text{Total work in one day} = \frac{4}{60} + \frac{2}{60} + \frac{1}{60} = \frac{7}{60} \]

### Step 4: Calculate the total time taken to complete the work together.
The total work can be considered as 1 unit of work. If they complete \(\frac{7}{60}\) of the work in one day, the total time taken (T) to complete 1 unit of work is:
\[ T = \frac{\text{Total work}}{\text{Total work in one day}} = \frac{1}{\frac{7}{60}} = \frac{60}{7} \text{ days} \]

### Final Answer:
Thus, A, B, and C together will complete the work in \(\frac{60}{7}\) days, which is approximately 8.57 days.

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