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

Options

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

Answer

To solve the problem of how many days A, B, and C can complete a piece of work together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Work Rate of Each Person:**
- A can complete the work in 10 days, so A's work rate is:
\[ \text{Work rate of A} = \frac{1}{10} \text{ (work per day)} \]
- B can complete the work in 20 days, so B's work rate is:
\[ \text{Work rate of B} = \frac{1}{20} \text{ (work per day)} \]
- C can complete the work in 60 days, so C's work rate is:
\[ \text{Work rate of C} = \frac{1}{60} \text{ (work per day)} \]

2. **Add the Work Rates Together:**
- To find the combined work rate of A, B, and C, we add their individual work rates:
\[ \text{Combined work rate} = \frac{1}{10} + \frac{1}{20} + \frac{1}{60} \]

3. **Find a Common Denominator:**
- The least common multiple (LCM) of 10, 20, and 60 is 60. We will convert each fraction to have a denominator of 60:
\[ \frac{1}{10} = \frac{6}{60}, \quad \frac{1}{20} = \frac{3}{60}, \quad \frac{1}{60} = \frac{1}{60} \]

4. **Combine the Fractions:**
- Now we can add the fractions:
\[ \text{Combined work rate} = \frac{6}{60} + \frac{3}{60} + \frac{1}{60} = \frac{10}{60} \]
- Simplifying this gives:
\[ \frac{10}{60} = \frac{1}{6} \]

5. **Calculate the Total Time to Complete the Work:**
- The combined work rate of A, B, and C is \(\frac{1}{6}\), which means together they can complete \(\frac{1}{6}\) of the work in one day. Therefore, the total time taken to complete the work is the reciprocal of the combined work rate:
\[ \text{Total time} = \frac{1}{\frac{1}{6}} = 6 \text{ days} \]

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

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