give solution plz

Question

A can do a job in 15 minutes,B takes 20 minutes while C takes 30 minutes to do the same job. All three begin working together.A leaves after 2 minutes, leaving B and C to continue working together.B leaves 4 minutes after that, leaving C to finish the job.How much more time will C take to finish the job?

Answer 1

The total work completed after 2min is:  2/15 + 2/20 + 2/30 

The total work completed after 6min is:   2/15 + 6/20 + 6/30   as A has already left.  This is also the time B leaves.

 

2/15 + 6/20 + 6/30 = (8+18+12)/60 = 38/60 = 19/30

 

Since C completes 1/30 per minute, C will need (30/30-19/30) / (1/30) = (11/30) / (1/30) =  11 minutes to complete the task.

Answer 2

Portion of job done by A in 1 minute = 1/15

   So, portion of job done by A = 2(1/15) = 2/15

 

Portion of job done by B in 1 minute = 1/20

   So, portion of job done by B = 6(1/15) = 2/5

 

Portion of job done by C in 1 minute = 1/30

   So, portion of job done by C = (x+6)(1/30), where x is the number of minutes that C works after B stops working.

 

Therefore, 2/15 + 2/5 + (x+6)/30 = 1

 

Multiply by the LCD, 30, to get 4 + 12 + x+6 = 30

 

                                                          x + 22 = 30

 

                                                                x = 8 minutes