Answer:
5 days
Step-by-step explanation:
Number of days taken by B for completion of the work = 45 days.
Efficiency of A is thrice that of B hence he will complete the same task in [tex]\frac{1}{3}[/tex] rd time of B
Hence number of days A takes to finish the same job = [tex]\frac{45}{3}[/tex] = 15 days.
Also
Efficiency of A is half that of C , Hence C takes half the time A takes to finish the job. Hence number of days taken by C to Finish the same job = [tex]\frac{15}{2}[/tex] days
Now,
Amount of work completed by A in a single day =[tex]\frac{1}{15}[/tex]
Amount of work completed by C in a single day = [tex]\frac{2}{15}[/tex]
If A and C works together the amount of work completed =[tex]\frac{1}{15} + \frac{2}{15}[/tex]
= [tex]\frac{3}{15}[/tex]
= [tex]\frac{1}{5}[/tex]
Hence the number of days taken to finish the job together by A and C = 5 days
