A finishes a work in 18 days, B in 15 days. B works for 10 days and leaves. In how many days will A alone finish the remaining work?

Problem restatement
With different solo times for A and B, B contributes for 10 days first. Compute the leftover work for A and the time needed.

Given data

• A's time = 18 days → A's rate = 1/18 job/day.
• B's time = 15 days → B's rate = 1/15 job/day.
• B works 10 days.

Concept/Approach
Work done = rate × time. Remaining = 1 − (B's contribution).

Step-by-step calculation
Work by B in 10 days = 10 × (1/15) = 2/3 Remaining work = 1 − 2/3 = 1/3 Time for A = (1/3) ÷ (1/18) = 6 days

Verification
Equivalent unit method: LCM 90 units. B does 6 units/day × 10 = 60; remaining 30 units; A does 5/day → 6 days.

Common pitfalls

• Subtracting days instead of subtracting work.

Final Answer
6 days