A can do a job in 15 days, B in 10 days and C in 30 days. If A is helped by B and C on every third day, then the job will be completed in

Options

A. `6 (1)/(3)` days
B. `8 (1)/(3)` days
C. 8 days
D. 9 days

Answer

To solve the problem step by step, we will calculate the work done by A, B, and C, and how they contribute to completing the job over a period of days.

### Step 1: Determine the work done by A, B, and C in one day.

- A can complete the job in 15 days, so in one day, A does:
\[ \text{Work done by A in one day} = \frac{1}{15} \text{ of the job} = 2 \text{ units} \]

- B can complete the job in 10 days, so in one day, B does:
\[ \text{Work done by B in one day} = \frac{1}{10} \text{ of the job} = 3 \text{ units} \]

- C can complete the job in 30 days, so in one day, C does:
\[ \text{Work done by C in one day} = \frac{1}{30} \text{ of the job} = 1 \text{ unit} \]

### Step 2: Calculate the total work done in a cycle of 3 days.

- **Day 1**: A works alone:
\[ \text{Total work done on Day 1} = 2 \text{ units} \]

- **Day 2**: A works alone:
\[ \text{Total work done on Day 2} = 2 \text{ units} \]

- **Day 3**: A, B, and C work together:
\[ \text{Total work done on Day 3} = 2 + 3 + 1 = 6 \text{ units} \]

### Step 3: Calculate the total work done in 3 days.

- Total work done in 3 days:
\[ \text{Total work in 3 days} = 2 + 2 + 6 = 10 \text{ units} \]

### Step 4: Determine how many cycles are needed to complete the job.

- The total work required is 30 units. Since 10 units are completed in 3 days, we can find out how many cycles are needed:
\[ \text{Number of cycles} = \frac{30 \text{ units}}{10 \text{ units/cycle}} = 3 \text{ cycles} \]

### Step 5: Calculate the total time taken to complete the job.

- Since each cycle takes 3 days, the total time taken to complete 3 cycles is:
\[ \text{Total time} = 3 \text{ cycles} \times 3 \text{ days/cycle} = 9 \text{ days} \]

### Conclusion:

The job will be completed in **9 days**.

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