Three men A, B and C complete a work in 10 days, 12 days and 15 days respectively. All three of them start the work together. Aft…

Question

Three men A, B and C complete a work in 10 days, 12 days and 15 days respectively. All three of them start the work together. After 2 days A left and after next 2 days C also left. Find in how many more days the whole work will be completed?

1. A. 6 days
2. B. 6 2/5 days (Correct answer)
3. C. 6 3/5 days
4. D. 6 4/5 days

Correct Answer

Option B — 6 2/5 days

Detailed Solution & Explanation

The correct answer is 6 2/5 days.

Key Points

• Total work = LCM(10, 12, 15) = 60 units; rates are A = 6, B = 5, C = 4 units/day.
• First 2 days all three work: (6+5+4)×2 = 30 units. Next 2 days B and C work (A has left): (5+4)×2 = 18 units — 48 units done.
• Remaining 12 units are done by B alone: 12 ÷ 5 = 2.4 days. Total = 2 + 2 + 2.4 = 6 2/5 days.

Exam tip

• Convert each worker's rate to a per-day fraction, add the rates of those working in each stage, and track the work stage by stage.

Additional Information

• Taking total work as LCM(10, 12, 15) = 60 units turns fractions into whole numbers: A does 6, B does 5 and C does 4 units a day.
• The LCM method is almost always faster and less error-prone than working with 1/10 + 1/12 + 1/15.
• Combined rate = 15 units a day, so all three together would finish in 4 days; the extra time comes from someone leaving partway.