Since we have given that
Number of hours in which A can finish a job = 12 hours
Number of hours in which B can finish a job = 14 hours
Total work = L.C. M of (A’s hours, B’s hours)=L.C.M. of (12,14)=84 units
Number of units done by A = 84/12 = 7
Number of units done by B = 84/14 = 6
Since A and B working alternatively starting with ‘A’.
So, 7+6 = 13 units done in 2 days by A and B alternatively.
And we need to done 84 units of work.
First we try to find the multiple of 13 which is nearest to 84. i.e. 78 units
if 13 units done in 2 days then,
78 units done in 2/13 x 78 = 12days
6 days of A and 6 days of B.
So, After 12 days, the turn will be of A’s.
So, Remaining units will be done by A only.
A will do 6 units of work in 6/7days
Total days taken by A is 6×6/7
Cost per hour for A = Rs. 50
So, Total amount earned by A is 6 x6/7 x 50
48/7 x 50 = 342.85