Question

A can do a piece of work in 18 days and B in 12 days. they began the work together , but B left the work 3days before its completion. in how many days , in all was the work completed

Answer 1

let the total work is X
A does X/18 of work in a day
B does X/12 of work in a day
in 3 days A and B complete 3(1/18+1/12)X of work
=X(1/6+1/4)
=5X/12

remaining work is 7X/12

A will complete it in 18×7÷12 = 10.5 days

the all work is completed in 13 and half days

Answer 2

- 3 days before completion means B only did 9/12 of his work leaving 3/12 undone and should be done by A.

- A has to therefore do (18/18 + 3/12 = 1 1/4) of the work.

- now, if B does 1/18 of work in 1 day;

1 1/4 of work = (1 1/4)/1/18
     
                = 22 1/2 days
hence it took 22 1/2 days to do all the work to completion.