A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the work.
Number of days A required do a piece of work : 16
Number of days B required do a piece of work : 12
Work done by A in one day: 
Work done by B in one day: 
A works alone for 2 days, so work completed by A in 2 days : 
= 
Work left = 
Work done by A and B together in one day: 
= 
They can do the work together in 
days .
But 
th of the work is done by both A and B
Time required to complete 
th of the work together by A and B : 
6 days
Time taken to finish the work 6 + 2 = 8days ( here 2 is added because 
work is done by A alone).
Total time taken to finish the work: 8days