A can complete a particular task in 20 days whereas B can complete that task in 10 days. Both worked together for 4 days and then B leaves the task, then how many days will A take to complete the remaining task ?

Question

Accepted Answer

To determine how many days A will take to complete the remaining task after B leaves, we need to follow these steps:

1. **Calculate the work done by A and B together in 4 days:**

- A's rate of work is 1/20 of the task per day.
   - B's rate of work is 1/10 of the task per day.
   - Together, A and B can complete (1/20 + 1/10) of the task per day.
   - Simplifying, (1/20 + 1/10) = (1/20 + 2/20) = 3/20 of the task per day.

In 4 days, they complete 4 * (3/20) = 12/20 = 3/5 of the task.

2. **Determine the remaining work:**

- The total task is 1 (or 100%).
   - Work completed in 4 days is 3/5.
   - Remaining work = 1 - 3/5 = 2/5 of the task.

3. **Calculate how long A will take to complete the remaining work:**

- A completes 1/20 of the task per day.
   - To complete 2/5 of the task, A will take (2/5) / (1/20) days.
   - Simplifying, (2/5) / (1/20) = (2/5) * (20/1) = 40/5 = 8 days.

Therefore, A will take 8 days to complete the remaining task, which supports Option 4 as the correct answer.

**Explanation of why other options are incorrect:**

- **Option 1 (12 Days):** This option suggests that A would take 12 days to complete the remaining task. However, as calculated, A only needs 8 days to finish the remaining 2/5 of the task, not 12 days.

- **Option 2 (4 Days):** This option implies that A would complete the remaining task in 4 days. Given A's work rate, 4 days would only allow A to complete 4/20 = 1/5 of the task, which is insufficient to finish the remaining 2/5 of the task.

- **Option 3 (6 Days):** This option suggests that A would take 6 days to complete the remaining task. In 6 days, A would complete 6/20 = 3/10 of the task, which is still less than the required 2/5 (or 4/10) of the task.

Thus, Option 4 is the only correct answer, as A will indeed take 8 days to complete the remaining task.