Question from IT foundation. A can do a work in 20 days and B can do in 30 days. both of them start the work together and work for sometime then B leaves if A complete the remaining work in 10 days. find number of days which they worked together?

Work done by A in 1 days=1/20

Work done by A in 10 days=1/20×10                                                 =1/2

Total work done by A and B together=1-1/2=1/2

Work done by A and B together in 1  day=1/20+1/30

             =1/12

Time taken by A and B together to do 1/2 part of work=1/2÷1/12

                             =1/2×12/1

                              =6

Number of days for which they work together is equal to 6