A can finish a job in 24 days, B in 9 days, and C in 12 days. B and C work together for 3 days; A completes the remainder. How many days does A take for the remainder?

Problem restatement
Two faster workers (B, C) start and then leave; compute remaining work for A and the time A needs.

Given data

• A's rate = 1/24 job/day.
• B's rate = 1/9 job/day.
• C's rate = 1/12 job/day.
• B and C work together for 3 days.

Concept/Approach
First compute the fraction completed by (B + C) in 3 days, subtract from 1 to get the remainder, then divide by A's rate.

Step-by-step calculation
(B + C) rate = 1/9 + 1/12 = 7/36 Work done in 3 days = 3 × (7/36) = 7/12 Remainder = 1 − 7/12 = 5/12 Time for A = (5/12) ÷ (1/24) = (5/12) × 24 = 10 days

Verification
Unit-check: 10 days at 1/24 per day completes 10/24 = 5/12, equal to the remainder.

Common pitfalls

• Multiplying instead of dividing by A's rate when converting remainder to time.

Final Answer
10 days