A, B & C can independently do a job in 15,20 and 30 days. they work together for some time after which C leave .a total of 18000/- is paid for the work & B gets 6000 more than C. for how many days did A work ?

Hi,

Let the total work to be done be 60 units.

So, A must do 4 units/day, B 3 units/day and C 2 units/day.

A and B must have done work on equal number of days. So, their salaries must be in the ratio 3:4.

Lets suppose B gets 3x salary. So, A gets 4x salary and C 3x-6000.

=> 3x-6000+3x+4x=18000

=> x = 2400

So, C's total salary will be 3 X 2400 - 6000 = 1200

So in the days C worked, B and A must get 1800 and 2400 salaries i.e. a total of Rs 5400.

=> Work done in these days is 5400/18000 = 54/180 = 3/10 or 18 units of work.

18 units of work can be completed by them in 2 days together.

The rest of the 42 units of the work can be completed by A and B in 6 days.

So, A worked for a total of 6+2 = 8 days