Shortcut Trick Total work done by A, B, and C in two days is ⇒ 2(6 + 5 + 4) ⇒ 30 unit Remaining work is ⇒ 60 - 30 ⇒ 30 unit The remaining work done by B in the number of days is ⇒ 30/5 ⇒ 6 days The total number of days to complete the work is ⇒ (6 + 2) days ⇒ 8 days ∴ The required number of days to complete the work is 8 days. Traditional method: Given: A can do a piece of work in 10 days B can do a piece of work in 12 days C can do a piece of work in 15 days A and C left after two days Calculations: Let the total work be 1 unit According to the question, we have Work done by A in 1 day is 1/10 unit Work done by B in 1 day is 1/12 unit Work done by C in 1 day is 1/15 unit Now, Total work done by A, B and C in two days is ⇒ 2{(1/A) + (1/B) + (1/C)} ⇒ 2{(1/10) + (1/12) + (1/15)} ⇒ 2{(6 + 5 + 4)/60} ⇒ 2 × (15/60) ⇒ 1/2 unit work is completed Remaining work is ⇒ {1 - (1/2)} ⇒ 1/2 unit The number of days required to complete 1/2 unit work by B is ⇒ (1/2) × 12 ⇒ 6 days The total number of days to complete the work is ⇒ (6 + 2) days ⇒ 8 days ∴ Required number of days to complete the work is 8 days.