A completes 80% of a work in 20 days. A and B together finish the remaining work in 3 days. How long would B alone take to do the whole work?

Problem restatement
From A's partial-completion time and the joint finishing time with B, find B's solo time for the entire job.

Given data

• A completes 80% (0.8) in 20 days → A's rate = 0.8/20 = 0.04 = 1/25 job/day.
• Remaining work = 20% = 0.2.
• (A + B) finish 0.2 in 3 days → (A + B) rate = 0.2/3 = 1/15 job/day.

Concept/Approach
Compute B's rate by subtracting A's rate from the combined rate, then invert to get B's time for 1 job.

Step-by-step calculation
A's rate = 1/25 (A + B) rate = 1/15 B's rate = 1/15 − 1/25 = (5 − 3)/75 = 2/75 job/day B's time = 1 ÷ (2/75) = 75/2 = 37.5 days

Verification/Alternative
Check the finish segment: In 3 days, A contributes 3 × 1/25 = 0.12; B contributes 3 × (2/75) = 0.08; total = 0.20 (the remaining 20%).

Common pitfalls

• Assuming A's 20-day time is for the full job; it is for 80% only.
• Subtracting times instead of subtracting rates to get B's speed.

Final Answer
37.5 days