Amit can complete a piece of work alone in 25 days, and Punit can complete the same work alone in 20 days. Punit works alone on the job for 10 days and then leaves. In how many days will Amit alone complete the remaining work?

Introduction / Context:
This is a two-person time and work problem where one worker (Punit) starts the work and the other worker (Amit) finishes it. We are given how long each worker would take individually to complete the full job, and we know the amount of time Punit works before leaving. The goal is to determine the additional time Amit needs to finish the remaining part of the job on his own.

Given Data / Assumptions:

• Amit alone can complete the work in 25 days.
• Punit alone can complete the same work in 20 days.
• Punit works alone for 10 days and then leaves.
• Amit finishes the remaining work alone.
• Total work is considered as 1 unit.
• All work rates are constant.

Concept / Approach:
We first calculate how much work Punit completes in 10 days using his individual work rate. Subtract this from the total work to find the remaining amount. Then we use Amit's work rate to compute how long it will take him to finish that remaining portion. This approach is direct and uses the basic formula: work done = rate * time.

Step-by-Step Solution:
Step 1: Let total work be 1 unit. Step 2: Punit can complete the work in 20 days, so his rate = 1/20 units per day. Step 3: In 10 days, the amount of work done by Punit = 10 * (1/20) = 10/20 = 1/2 of the job. Step 4: Remaining work after Punit leaves = 1 - 1/2 = 1/2 of the job. Step 5: Amit can complete the full work in 25 days, so his rate = 1/25 units per day. Step 6: Time taken by Amit to complete the remaining 1/2 of the work = (1/2) / (1/25). Step 7: Simplify the expression: (1/2) / (1/25) = 1/2 * 25 = 25/2 = 12.5 days.

Verification / Alternative check:
We can check by computing the work done by Amit in 12.5 days. At rate 1/25 units per day, Amit does 12.5 * (1/25) = 12.5 / 25 = 1/2 of the job, which matches the remaining amount. Thus, Punit does the first half of the job, and Amit does the second half, so together they complete the full job as required.

Why Other Options Are Wrong:

• 10.5 days, 11.5 days, and 13.5 days all correspond to incorrect calculations of Amit's time or misunderstanding of how much work Punit completed.
• Any value other than 12.5 days would imply that Amit either over-completes or under-completes the remaining half of the work.

Common Pitfalls:
Some students mistakenly think that since Punit works for half of his required time (10 out of 20 days), he must have done half the work, which is actually correct here but should always be checked using rate * time. Others may average the days of Amit and Punit or add them directly, which does not reflect the actual work distribution. Always compute the exact work done by each person using rates and time intervals.

Final Answer:
Amit will take 12.5 days to complete the remaining work alone.