A can finish a piece of work in 16 days, B in 20 days,

Solution

Let the total work be 1 unit. A’s efficiency = 1/16, B’s efficiency = 1/20, and C’s efficiency = 1/24. A works alone for the first 4 days: Work done by A in 4 days = 4 × 1/16 = 1/4. Remaining work = 1 - 1/4 = 3/4. A and B work together for 2 more days: Work done by A and B in 2 days = (1/16 + 1/20) × 2 = (9/80) × 2 = 9/40. Remaining work = 3/4 - 9/40 = 30/40 - 9/40 = 21/40. Now, A, B, and C are working together. Their combined efficiency = 1/16 + 1/20 + 1/24 = 37/240. Time taken to complete the remaining work = (21/40) ÷ (37/240) = 126/37  ≈ 3.4 days. Final Answer: (b) 3.4 days