A can build up a structure in 8 days and 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 structure ?

Explanation:

A’s 1 day’s work = 1/8

B’s 1 day’s work in breaking the building

= 1/3

Now, according to the question,

A’s 4 day’s work = 4×1/8=12

Now, A’s and B’s 2 day’s work

=2(1\8−1\3)=2×−5/24=−10\24

Total work done in 6 days

1\2+(−10\24)=12−10\24=1\12

Remaing work = 1−1\12=11\12

Now, A has to complete the work, so A can complete in x days.

18×x=11\12=> x=11×8\12

x=11×2\3=7 1\3days.