A can finish a work alone in 5 days. With the help of his friend, the same work finishes in 3 days. In how many days can the friend alone complete the work?

Introduction / Context:
When two people together complete faster than one person alone, the partner’s rate equals the joint rate minus the known individual rate. Invert the partner’s rate to get the partner’s time alone.

Given Data / Assumptions:

• A alone = 5 days → rate 1/5.
• Together = 3 days → rate 1/3.

Concept / Approach:
Friend’s rate = (1/3) - (1/5). Time = 1 / (friend’s rate).

Step-by-Step Solution:

Verification / Alternative check:
Combined check: 1/5 + 2/15 = 3/15 + 2/15 = 5/15 = 1/3 → matches together time 3 days.

Why Other Options Are Wrong:
They do not satisfy the rate difference or inverse relationship implied by the given data.

Common Pitfalls:
Subtracting times instead of rates; forgetting to invert the final rate to get time.

Final Answer:
7 1/2 days