A and B can complete a task in 12 days and 18 days, respectively. They begin the work together, but B leaves after 4 days. How many more days will A take to finish the remaining work?
\(5\tfrac{1}{3}\) days
Take total work as the LCM of 12 and 18, i.e., 36 units.
Step 1 – Per-day rates:
A: \(\dfrac{36}{12} = 3\) units/day; B: \(\dfrac{36}{18} = 2\) units/day.
Step 2 – Work done together in 4 days:
\((3 + 2) \times 4 = 20 \text{ units}\).
Step 3 – Remaining work and time for A:
Remaining = \(36 - 20 = 16\) units.
A's time = \(\dfrac{16}{3} = 5\tfrac{1}{3}\) days.
Hence A needs \(5\tfrac{1}{3}\) more days.
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