A, B and C can finish a job working alone in 20 days, 30 days and 60 days respectively. They all work together for 1 full day, and then only C continues working alone. How many days will C alone take to finish the remaining part of the job?

Introduction / Context:
This problem combines individual work rates with a short initial period of teamwork followed by one person completing the remaining job. It is a standard pattern in time and work questions that teaches you how to account for partial completion by a group and then compute how long one worker, here C, will take to complete what is left.

Given Data / Assumptions:

• A alone can finish the job in 20 days.
• B alone can finish the job in 30 days.
• C alone can finish the job in 60 days.
• All three work together for exactly 1 day.
• After that, A and B stop working and only C continues until the job is finished.
• Work rate is constant for each person.

Concept / Approach:
We treat the total job as 1 unit of work. Each person has a daily work rate equal to 1 divided by the number of days they take. First, we calculate the combined rate of A, B, and C to see how much of the job is done in that one day. Then we subtract that from 1 to find the fraction that remains. Finally, using C's individual rate, we calculate the extra days needed for C to finish the remaining work alone.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. Step 2: Daily rate of A = 1/20, of B = 1/30, and of C = 1/60. Step 3: Combined rate of A + B + C = 1/20 + 1/30 + 1/60. Step 4: Compute this sum: 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10. Step 5: In one day they complete 1/10 of the work, so remaining work = 1 − 1/10 = 9/10. Step 6: C alone works at 1/60 of the job per day. Step 7: Time taken by C to complete 9/10 = (9/10) / (1/60) = (9/10) × 60 = 54 days.

Verification / Alternative check:
We can estimate: C is the slowest worker, taking 60 days for the full job. Since about 90 percent of the job is still left (9/10), a time very close to 0.9 × 60 = 54 days is expected. Our exact calculation also gives 54 days, so the result is consistent. Nothing in the calculation conflicts with the original data, so the answer is verified.

Why Other Options Are Wrong:
48 days would mean C completes 48/60 = 4/5 of the job, which is less than the 9/10 that remains. 45 and 36 days similarly correspond to even smaller fractions of the work. 60 days would be the time for C to do the entire work alone, not just the remaining 9/10. Therefore, none of these matches the required remaining fraction, and only 54 days is correct.

Common Pitfalls:
A common mistake is to miscompute the combined rate of the three workers, especially when converting to a common denominator. Another is to forget that the team works for only 1 day, not until the work is half or fully done. Some learners also incorrectly subtract C's work twice when calculating the remaining fraction. Keeping a clear structure of total work, work done, and work left avoids these errors.

Final Answer:
C will take 54 days to finish the remaining work alone.