A, B and c can complete a piece of work in 10, 20 and 60 days respectively. Working together can complete the same work in how many days?

Options

A. 5
B. 6
C. 10
D. 8

Answer

To find out how many days A, B, and C can complete the work together, we will follow these steps:

### Step 1: Determine the work done by each person in one day.
- A can complete the work in 10 days. Therefore, in one day, A can complete:
\[ \text{Work done by A in one day} = \frac{1}{10} \text{ of the work} \]

- B can complete the work in 20 days. Therefore, in one day, B can complete:
\[ \text{Work done by B in one day} = \frac{1}{20} \text{ of the work} \]

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

### Step 2: Calculate 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 contributions:
\[ \text{Total work in one day} = \frac{1}{10} + \frac{1}{20} + \frac{1}{60} \]

### Step 3: Find a common denominator and add the fractions.
The least common multiple (LCM) of 10, 20, and 60 is 60. We will convert each fraction to have a denominator of 60:
\[ \frac{1}{10} = \frac{6}{60}, \quad \frac{1}{20} = \frac{3}{60}, \quad \frac{1}{60} = \frac{1}{60} \]
Now, adding these fractions:
\[ \text{Total work in one day} = \frac{6}{60} + \frac{3}{60} + \frac{1}{60} = \frac{10}{60} = \frac{1}{6} \]

### Step 4: Calculate the total time taken to complete the work.
If A, B, and C together complete \(\frac{1}{6}\) of the work in one day, then the total time taken to complete the entire work is:
\[ \text{Total time} = \frac{1}{\frac{1}{6}} = 6 \text{ days} \]

### Final Answer:
A, B, and C together can complete the work in **6 days**.

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