A can complete a job in 20 days. Every third day, he is assisted by B who can complete the job alone in 30 days. In how many days will the job be completed?

Explanation

Given: ​ A’s time = 20 days Copyright © 2026 Adda247 B’s time = 30 days Assistance schedule: Every 3rd day. Solution: Calculate Efficiency (Units per Day). Let Total Work = LCM (20, 30) = 60 units. 60 60 A= = 3 u/d, B= = 2 u/d. 20 30 ​ ​ Analyze 3-day Cycle. Day 1: A works = 3 units Day 2: A works = 3 units (A + B) work = 3 + 2 = 5 units Total work in 3 days = 3 + 3 + 5 = 11 units. Calculate full cycles. 60 = 5 cycles, Remainder = 5 units. 11 ​ Time for 5 cycles = 5 × 3 = 15 days. Work done = 55 units. Complete Remaining Work (5 units). Day 16 (A works): Does 3 units. Remainder = 5 − 3 = 2. Day 17 (A works): Needs to do 2 units. 2 Time taken = day. 3 ​ 2 2 Total Time = 15 + 1 + = 16 days. 3 3 ​ ​ Final Answer 2 16 days​ 3 ​