One-day head start by A, then both finish the job A completes a work in 15 days and B in 20 days. A works alone for 1 day, then A and B work together to finish. How many additional days are needed after the first day?

Introduction / Context:
Problems with an initial solo day followed by joint work are solved by subtracting the first day’s contribution and then dividing the remainder by the combined daily rate.

Given Data / Assumptions:

• A alone: 15 days ⇒ 1/15 per day.
• B alone: 20 days ⇒ 1/20 per day.
• A works alone for 1 day; then both work together.

Concept / Approach:
Remaining fraction = 1 − 1/15. Combined rate = 1/15 + 1/20.

Step-by-Step Solution:

Verification / Alternative check:
Total time = 1 + 8 = 9 days; check: 9 * (1/15) + 8 * (1/20) = 0.6 + 0.4 = 1 job.

Why Other Options Are Wrong:
7 or 6 days leave unfinished work; “None of these” is unnecessary because 8 is exact.

Common Pitfalls:
Forgetting that the question asks for additional days after the first solo day.

Final Answer:
8 days