Question

A can do a work in 14 days,B can do the same work in 13 days,then in how many days can A and B together finished the work?

Answer 1

in 13.5days a n b can complete the work

Answer 2

Time taken by A to complete the work = 14 days
Part of work completed by A in one day = 1/14

Time taken by B to complete the work = 13 days
Part of work completed by B in one day = 1/13

So,
The work completed in one day when both of them work together  
= 1/14 + 1/13
= 27 / 182

So,
The time taken by both to complete the work when both of them work together = 182 / 27 
$= 6 \frac{20}{27} days$