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.
Answer & explanation
Correct answer: option 2
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