Ranjith can complete a task in 25 days while Anji can finish the same task in 20 days. They work together on the task for 5 days, after which Ranjith leaves. In how many additional days will Anji alone finish the remaining work?

Introduction / Context:
This time and work problem considers two workers, Ranjith and Anji, who work together initially and then only one of them continues to complete the remaining work. We are asked to determine how long the second worker, Anji, will need to finish the task alone once the other leaves. This setup is typical in aptitude tests and helps build understanding of fractional completion and remaining work calculations.

Given Data / Assumptions:

• Ranjith can complete the task alone in 25 days.
• Anji can complete the same task alone in 20 days.
• They work together for 5 days.
• Then Ranjith leaves, and Anji alone finishes the remainder.
• Total work is taken as 1 complete job.
• Work rates of both workers remain constant.

Concept / Approach:
We convert each worker time into a daily work rate, expressed as job per day. Then we compute how much work is completed during the initial period when both work together. Subtracting this from the total yields the remaining work. Finally, we divide the remaining work by Anji daily rate to find the number of additional days required for Anji to finish the task alone. This is a direct application of basic rate and time relationships.

Step-by-Step Solution:
Step 1: Let total work be 1 job. Step 2: Ranjith daily rate = 1/25 job per day. Step 3: Anji daily rate = 1/20 job per day. Step 4: Combined daily rate when both work together = 1/25 + 1/20. Step 5: LCM of 25 and 20 is 100, so 1/25 = 4/100 and 1/20 = 5/100. Step 6: Combined rate = (4/100 + 5/100) = 9/100 job per day. Step 7: Work done together in 5 days = 5 * (9/100) = 45/100 = 9/20 of the job. Step 8: Remaining work = 1 - 9/20 = 11/20 of the job. Step 9: Anji daily rate is 1/20, so time needed by Anji alone = (11/20) / (1/20) = 11 days.

Verification / Alternative check:
We can verify by checking total contributions. During the first 5 days, both together complete 9/20 of the task. If Anji then works for 11 more days at 1/20 job per day, she completes 11/20 of the task. Adding these gives 9/20 + 11/20 = 1 full job, confirming that the work is exactly completed with the calculated schedule. Thus, 11 days is the correct additional time for Anji alone.

Why Other Options Are Wrong:
If Anji took only 9 or 10 days, the total work done would add up to less than 1 job. If she took 12 or 15 days, the total work would exceed one full job. Therefore, these times would not match the exact completion of the task. Only 11 days gives a total of exactly one complete job when combined with the first 5 days of joint work.

Common Pitfalls:
A typical error is to treat the time for the joint work period as if it were done by one person alone, which leads to incorrect remaining work. Some learners also forget to use a common denominator while adding rates or computing fractional work. Proper handling of fractions and careful subtraction of completed work from the total are essential steps to avoid mistakes.

Final Answer:
Anji alone will take 11 more days to finish the remaining work after Ranjith leaves.