A can do a work in 6 days while b can do a work in 8 days. They worked together for 2 days and B left the work. How time will A require to complete the work?

Question

Help me with this question if unitary method. 

 

 

A can do a work in 6 days while b can do a work in 8 days. They worked together for 2 days and B left the work. How time will A require to complete the work?

Answer 1

A can do a work in 6 days while B can do a work in 8 days. 

 

6A = 1  {6 times A does 1 job}; so A = 1/6 {1/6 of job per day}

 

 

8B = 1  {8 times B does 1 job}; so B = 1/8 {1/8 of job per day}

 

They worked together for 2 days and B left the work.

 

2 x (1/6 + 1/8) = 1/3 + 1/4 = 4/12 + 3/12 = 7/12 {or 7/12 of the job is done in 2 days they work together}

 

This leaves 5/12 of the job remaining when B leaves.

 

How time will A require to complete the work?

 

Since A does 1/6 job per day we divide 1/6 into the remaining 5/12 or

 

[5/12] / [1/6] or  5/12 x 6/1 = 30/12 = 2.5 days

 

 

 

Answer 2

 X - number of days required that if both work together finish the task.

 

 

              1/ 6 + 1/8 = 1/X

 

               4/24 + 3/ 24  = 7/24  = 1/x

 

               X = 24/ 7 = 3 3/7    / days required if both work together to complete the task

 

                3 3/7 - 2 = 1 1/7   / days  left to finish the task, after B left, if work together

 

               (8/7) / (24/7) = 1/3  of task was left

 

      1/6 = (1/3 ) / X

 

       X = 2  needed to finish the job