A can complete a work in 15 days and B in 20 days. If both work together for 4 days, what fraction of the work remains unfinished?

Problem restatement
After 4 days of joint work, find the remaining fraction of the job.

Given data

• A's time = 15 days → rate = 1/15.
• B's time = 20 days → rate = 1/20.

Concept/Approach
Joint rate adds. Done in 4 days = 4 × (1/15 + 1/20). Remaining = 1 − (done).

Step-by-step calculation
Combined rate = 1/15 + 1/20 = (4 + 3)/60 = 7/60 Work done in 4 days = 4 × (7/60) = 28/60 = 7/15 Remaining fraction = 1 − 7/15 = 8/15

Verification
Convert to a common denominator if needed to avoid arithmetic slips.

Common pitfalls

• Mistakenly averaging times (15 and 20) instead of adding rates.

Final Answer
8/15