A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall?Options13 days7 1/3 days13 1/3 days7 days

To solve this problem, we first need to understand the rate at which A and B work.

1. A can build a wall in 8 days. So, A's work rate is 1 wall/8 days = 1/8 of the wall per day.
2. B can break a wall in 3 days. So, B's work rate is -1 wall/3 days = -1/3 of the wall per day (negative because B is breaking the wall).

Next, we calculate how much of the wall is built after A works for 4 days and then A and B work together for 2 days.

1. In 4 days, A can build 4 * (1/8) = 1/2 of the wall.
2. When A and B work together, their combined work rate is (1/8 - 1/3) = -1/24 of the wall per day. So, in 2 days, they can build 2 * (-1/24) = -1/12 of the wall. Since this is negative, it means that they actually break 1/12 of the wall.

So, after 6 days (4 days of A working and 2 days of A and B working together), 1/2 - 1/12 = 5/12 of the wall is built.

Finally, we calculate how long it will take A to build the remaining part of the wall.

1. The remaining part of the wall is 1 - 5/12 = 7/12.
2. Since A's work rate is 1/8 of the wall per day, it will take A (7/12) / (1/8) = 7 * (8/12) = 56/12 = 4 2/3 days to build the remaining part of the wall.

So, the answer is 4 2/3 days. However, this option is not available in the given options. There might be a mistake in the problem or the options.