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15 Time & Work Questions and Answers
15 solved Time & Work questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.
Time and Work questions test your ability to calculate how long it takes to complete a task when individuals or groups work together or separately. The fundamental principle is that work done equals the product of rate (efficiency) and time. If a person completes a job in N days, their rate is 1/N of the work per day. When multiple people work together, their rates add up. Common variations include: work left incomplete by one person and finished by another, pipe and cistern problems (inlet and outlet), and efficiency-based comparisons. Below are 15 solved time and work questions with detailed step-by-step explanations.
A can complete a task in 13 days. After working alone for 6 days, how many days of work remain?
A can finish a work in 10 days. What fraction of work does A complete in 4 days?
A can complete a task in 11 days. After working alone for 3 days, how many days of work remain?
A finishes a job in 15 days and B in 30 days. In how many days can they finish together?
A can finish a work in 15 days. What fraction of work does A complete in 6 days?
A can complete a task in 8 days. After working alone for 4 days, how many days of work remain?
A finishes a job in 12 days and B in 12 days. In how many days can they finish together?
A can complete a task in 17 days. After working alone for 7 days, how many days of work remain?
A can finish a work in 11 days. What fraction of work does A complete in 3 days?
A can complete a task in 11 days. After working alone for 4 days, how many days of work remain?
A finishes a job in 12 days and B in 24 days. In how many days can they finish together?
A can complete a task in 8 days. After working alone for 3 days, how many days of work remain?
A finishes a job in 8 days and B in 24 days. In how many days can they finish together?
A can complete a task in 19 days. After working alone for 5 days, how many days of work remain?
A finishes a job in 9 days and B in 18 days. In how many days can they finish together?
Key Takeaways
- Work rate = 1/Time. Faster worker = smaller time = larger rate.
- Combined rate = sum of individual rates. Never add times directly.
- LCM method simplifies complex work problems: convert everything to work units.
- For alternate-day work: track work done in each cycle of days, then count cycles.
Frequently Asked Questions
How do I calculate combined work rate?
Combined rate = Sum of individual rates. If A completes a job in 10 days (rate = 1/10) and B in 15 days (rate = 1/15): Combined rate = 1/10 + 1/15 = 1/6. Together they take 6 days.
What is the LCM method for time-work?
Take LCM of individual times to represent total work in units. If A takes 10 days and B takes 15 days: LCM = 30 units. A's efficiency = 3 units/day, B's = 2 units/day. Combined = 5 units/day. Time = 30 ÷ 5 = 6 days.
How do pipes and cisterns differ from regular work?
Inlet pipes fill (positive rate), outlet pipes drain (negative rate). Net rate = sum of inlet rates - sum of outlet rates. If an inlet fills a tank in 20 mins and an outlet drains it in 30 mins, net rate = 1/20 - 1/30 = 1/60. Time to fill = 60 minutes.
More Time & Work Practice Resources
For more time & work practice, try our timed quiz mode that generates fresh questions every session.