⏳ Time & Work
Time & Work is a common topic in competitive exams. Here are the important concepts, formulas, and examples you need to know:
📌 Basics
- If a person can complete a work in n days, then work done in 1 day = 1/n.
- If A can finish in a days and B in b days, then together they take (a × b) / (a + b) days.
- Wages are proportional to work done.
- Efficiency Method: Assume total work = LCM of days.
📌 Variations
- Work together, then one leaves: Calculate work done, subtract, and check remaining.
- Work + Negative Work (e.g., Pipes & Cisterns): Net work = Fill rate – Empty rate.
- Alternate Days: A works 1 day, B next day. Add 2-day cycle.
Time and Work – 20 Questions
Q1. A alone can do a work in 10 days. How many days will A take to complete half of the work?
Q2. A can do a work in 20 days, B in 30 days. Together, how many days will they take?
Q3. A does a piece of work in 15 days and B in 25 days. Together, in how many days can they complete it?
Q4. A, B, and C can finish a work in 12, 15, and 20 days respectively. How many days will they take together?
Q5. A and B together do a job in 6 days. B alone can do it in 18 days. How many days will A alone take?
Q6. A is twice as efficient as B. If A and B together finish a job in 12 days, how long will B alone take?
Q7. A can do a work in 10 days, B in 15 days, C in 30 days. Working together, how long will they take?
Q8. A does a work in 8 days, B in 12 days, and C in 24 days. They start together, but C leaves after 2 days. In how many days will the work finish?
Q9. A and B can finish a job in 18 days, B and C in 24 days, and A and C in 36 days. How many days will A, B, and C take together?
Q10. A, B, and C can complete a task in 12, 15, and 18 days respectively. They all start but A leaves after 2 days, B leaves after 3 days. How long will C take to finish the rest?
Q11. A pump can fill a tank in 6 hours. Due to a leak, it fills in 8 hours. In how many hours will the leak alone empty the full tank?
Q12. A cistern can be filled by a pipe in 10 hours and emptied by a drain in 15 hours. If both are opened together, in how much time will the cistern be full?
Q13. A and B can finish a work in 12 days. They worked together for 8 days, then A left. B finished the remaining work in 6 more days. How long will B alone take to finish the whole work?
Q14. A can do a work in 25 days, B in 20 days, and C in 30 days. They start together but C leaves after 5 days. In how many days will A and B complete the remaining work?