Adam and Bryan can complete a job in 48 hours working together.

Go step wise and you will get the answer..
Let the time be A and B for Adam and Bryan to complete a job alone, so \(\frac{1}{A}+\frac{1}{B}=\frac{1}{48}\)..

Step 1 : Adam worked alone for half the time Bryan takes to complete the work
So, Adam works for B/2 hours and he will complete the work in \(\frac{1}{A}*\frac{B}{2}\)

Step 2 : then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work.
So, Bryan works for A/3 hours and he will complete the work in \(\frac{1}{B}*\frac{A}{3}\)

Step 3 : When Bryan stopped, five-sixths of the work was done.
so \(\frac{B}{2A}+\frac{A}{3B}=\frac{5}{6}.....3B^2+2A^2=5AB.....2B^2+2A^2-4AB-AB+B^2=0.......2(B-A)^2+B(B-A)=0....(B-A)+(2B-2A+B)=0....(B-A)+(3B-2A)=0\)


So, two cases..
(I) B=A, then \(\frac{1}{B}+\frac{1}{B}=\frac{1}{48}\)....B=96
(II) 3B=2A or A=3B/2, then \(\frac{2}{3B}+\frac{1}{B}=\frac{1}{48}........\frac{5}{3B}=\frac{1}{48}..... B=\frac{48*5}{3}=16*5=80\)

C