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 ?

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 = \( \Large 4\times 1/8=\frac{1}{2} \)

Now, A's and B's 2 day's work

=\( \Large 2\left(\frac{1}{8}-\frac{1}{3}\right) \)=\( \Large 2\times -5/24=\frac{-10}{24} \)

Total work done in 6 days

\( \Large \frac{1}{2} \)+\( \Large \left(\frac{-10}{24}\right) \)=\( \Large \frac{12-10}{24}=\frac{1}{12} \)

Remaing work = \( \Large 1-\frac{1}{12}=\frac{11}{12} \)

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

\( \Large \frac{1}{8}\times x=\frac{11}{12} \)=> x=\( \Large \frac{11\times 8}{12} \)

x=\( \Large \frac{11\times 2}{3} \)=\( \Large  7\frac{1}{3} \)days.