Question

A factory employs 8 workers to complete building a motorbike in 2 days. As it is the holiday season, the workforce gets halved everyday until only 1 worker is left working on the motorbike. If so, how many days does he have to work alone to complete the rest of the build? (All workers have the same capacity to work.)

• A. 8 days
• B. 4 days
• C. 2 days
• D. 1 day

Answer 1

The correct option is C 2 days

Workers = M
Days = D
Amount of work one worker can do in one day = W

$⟹Workdone=M\times D\times W$

Now, 8 workers can build the entire motorbike in 2 days.

$⟹Totalwork=8\times 2\times W=16W$

$Day1:Workers\left(M\right)=8$

$Workdone=M\times D\times W=8\times 1\times W=8W$

$Workremaining=Totalwork-Workdone=16W-8W=8W$

$Day2:Workers\left(M\right)=8÷2=4$

$Workdone=M\times D\times W=4\times 1\times W=4W$

$Workremaining=Leftoverwork-Workdone=8W-4W=4W$

$Day3:Workers\left(M\right)=4÷2=2$

$Workdone=M\times D\times W=2\times 1\times W=2W$

$Workremaining=Leftoverwork-Workdone=4W-2W=2W$

$Day4:Workers\left(M\right)=2÷2=1$

$Workdone=M\times D\times W=1\times 1\times W=W$

$Workremaining=Leftoverwork-Workdone=2W-W=W$

"W" is the work done by 1 worker in 1 day.

Hence, if the remaining worker works for the 5th day as well, he will be able to complete the build.

Therefore, the last worker remaining spends 2 days (4th day and the 5th day) working to complete the rest of the build.