A is 3 times as productive as B. Together they can complete a job in 16.5 days. If C joins them after they have worked for 11 days then in how many days can they finish the rest of the job if C alone can do the job in 12 days.

\(2\frac{6 }{19}\) days

Let the work done by B  = x units/day

 Therefore work done by A will =  3x units/day

Total work = Efficiency  ×  Number of days 

 Total work per  = ( 3x + x ) =  4x units

Number of days = 16.5 days 

Total work = 4x × 16.5 = 66x units 

Work done by A and B together in 11 days = 4x × 11 = 44x units

Remaining work = ( 66x - 44x ) = 22x 

C completed whole work in 12 days , efficiency of C = \(\frac{66x}{12}\) = 5.5x unit/day

After 11 days C also joins A and B , so total efficiency = 4x + 5.5x = 9.5x

Time taken to complete the remaining work =  \(\frac{22x}{9.5x}\) = \(\frac{44}{19}\)

= \(2\frac{6 }{19}\) days