A can do a piece of work in 8 days, B can do it in 10 days and C can do it in 20 days. In how many days canA, BandCtogether complete the work?

Options

A. ` 3 (7)/(11) days `
B. `3 (5)/(11) days `
C. `3 (2)/(11) days `
D. `3 (9)/(11) days `

Answer

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

### Step 1: Determine the work done by each person in one day.
- A can complete the work in 8 days, so A's one day work is:
\[ \text{Work done by A in one day} = \frac{1}{8} \]

- B can complete the work in 10 days, so B's one day work is:
\[ \text{Work done by B in one day} = \frac{1}{10} \]

- C can complete the work in 20 days, so C's one day work is:
\[ \text{Work done by C in one day} = \frac{1}{20} \]

### Step 2: Add the work done by A, B, and C together in one day.
Now, we can find the total work done by A, B, and C together in one day:
\[ \text{Total work done in one day} = \frac{1}{8} + \frac{1}{10} + \frac{1}{20} \]

### Step 3: Find a common denominator.
The least common multiple (LCM) of 8, 10, and 20 is 40. We will convert each fraction to have a denominator of 40:
- For A:
\[ \frac{1}{8} = \frac{5}{40} \]
- For B:
\[ \frac{1}{10} = \frac{4}{40} \]
- For C:
\[ \frac{1}{20} = \frac{2}{40} \]

### Step 4: Add the fractions.
Now, we can add the fractions:
\[ \text{Total work done in one day} = \frac{5}{40} + \frac{4}{40} + \frac{2}{40} = \frac{11}{40} \]

### Step 5: Calculate the total time taken to complete the work.
If A, B, and C together can do \(\frac{11}{40}\) of the work in one day, then the number of days required to complete the entire work is the reciprocal of the total work done in one day:
\[ \text{Days to complete the work} = \frac{1}{\frac{11}{40}} = \frac{40}{11} \approx 3.64 \text{ days} \]

### Final Answer:
A, B, and C together can complete the work in approximately \( \frac{40}{11} \) days or about 3.64 days.

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