Quick answer: D. 18 days. When people leave a job at different times, split the timeline into phases and calculate the work completed in each phase.
SSC GD time-and-work question
A, B and C can complete a piece of work individually in 20 days, 30 days and 60 days respectively. They start working together. A leaves after 4 days, and B leaves 3 days before the work is completed. In how many days is the entire work completed?
A. 10 days B. 15 days C. 12 days D. 18 days
Full step-by-step solution
Step 1: Convert each completion time into a work rate. The least common multiple of 20, 30 and 60 is 60, so treat the entire job as 60 units. A completes 60 / 20 = 3 units per day, B completes 60 / 30 = 2 units per day, and C completes 60 / 60 = 1 unit per day. Working together, their combined rate is 3 + 2 + 1 = 6 units per day.
Step 2: Work out the first phase. All three work together for the first 4 days. They complete 4 x 6 = 24 units.
Step 3: Describe the remaining phases using the total time. Let the whole job take T days. A has already left. Since B leaves 3 days before the job is completed, B and C work together from day 4 to day T - 3. This middle phase lasts T - 7 days, and their combined rate is 2 + 1 = 3 units per day. C then works alone for the final 3 days, completing 3 x 1 = 3 units.
Step 4: Add the work in all phases and solve. The total work is 60 units:
24 + 3(T - 7) + 3 = 60
Expand and simplify: 24 + 3T - 21 + 3 = 60, so 3T + 6 = 60. Therefore 3T = 54 and T = 18 days.
Correct answer: D. 18 days.
Check the answer
In the first 4 days, all three complete 24 units. The middle phase lasts 18 - 7 = 11 days, so B and C complete 11 x 3 = 33 units. C works alone for the final 3 days and completes 3 units. The total is 24 + 33 + 3 = 60 units, exactly the whole job.
Common mistake to avoid
Do not assume B works until the end or count the final 3 days as a separate phase for all workers. After A leaves, B and C work together; in only the final 3 days does C work alone.