Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take 8/3 more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs, 450, then in how many days did A, B and C together complete the whole work?

CND
efficiency is there but day has not given so CND

Hi, the wages will be given in the ratio of the portion of work completed which in turn will be proportional to the efficiency of each person.
Now, out of 450, B gets 120. So assuming the combined efficiency of a, b and c to be 15x, we get the efficiency of B as 15x(120/450) = 4x, So the efficiency of A and C will be 15x-4x = 11x
Assume the efficiency of A = y => the efficiency of B = 11x-y
Now, working together B and C take 50% more number of days than A, B and C together take and A and B working together.
So time taken by B and C to finish the work together = 1/(4x+11x-y) = 1.5(15x) => y=5x
Hence, the efficiency of A, B and C will be 5x, 4x and 6x respectively.
Now, time taken by A and B will be 1/(5x+4x)=8/3+1/(15x)
=> 1/9x - 1/15x = 8/3 => 2/45x = 8/3 => x = (2/45)*(3/8) = 1/60
So the time taken by A, B and C = 1/15x = 60/15=4 days