'A' can build up a structure in 8 days and 'B' can break it in 3 days. 'A' worked building for 4 days and then 'B' joined and start breaking while 'A' kept building for another 2 days. In how many days will 'A' alone build up the remaining part of the structure?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{22}{3}\) days
A person who builds the whole structure in \(n\) days builds \(\frac{1}{n}\) of it in a day. Breaking is negative work, so when A and B work together their one-day work is A’s part minus B’s part.
A’s one-day work \(=\frac{1}{8}\); B breaks \(\frac{1}{3}\) a day
A alone for 4 days builds \(\displaystyle 4\times\frac{1}{8}=\frac{1}{2}\)
Together for 2 days: \(\displaystyle 2\times\left(\frac{1}{8}-\frac{1}{3}\right)=2\times\left(-\frac{5}{24}\right)=-\frac{5}{12}\), so \(\frac{5}{12}\) is pulled down
Part still standing \(\displaystyle =\frac{1}{2}-\frac{5}{12}=\frac{1}{12}\)
Part left to build \(\displaystyle =1-\frac{1}{12}=\frac{11}{12}\)
Days A needs \(\displaystyle =\frac{11}{12}\div\frac{1}{8}=\frac{11}{12}\times8=\frac{22}{3}\) days
Tip: The value \(\frac{11}{12}\) in Option (2) is the part of the structure left to build, not the number of days.