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30 Time & Work Questions and Answers
30 solved Time & Work questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.
Advanced time & work questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.
Key Formulas
Work = Time × Rate (Rate = efficiency)
If person takes T days: Rate = 1/T work per day
Combined Rate = Rate₁ + Rate₂ + ... (add rates, NOT times)
LCM method: Total Work = LCM of individual times
Pipe problems: Inlet = +ve rate, Outlet = -ve rate
Q1
Medium
A finishes a job in 15 days and B in 30 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/15 + 1/30. Time = 450/45 = 10 days.
Q2
Medium
A can finish a work in 12 days. What fraction of work does A complete in 2 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/12. In 2 days, work done = 2/12.
Q3
Medium
A can complete a task in 14 days. After working alone for 11 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 14 days total, remaining days after 11 days = 14 - 11 = 3.
Q4
Medium
A finishes a job in 12 days and B in 24 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/12 + 1/24. Time = 288/36 = 8 days.
Q5
Medium
A can complete a task in 12 days. After working alone for 7 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 12 days total, remaining days after 7 days = 12 - 7 = 5.
Q6
Medium
A can finish a work in 15 days. What fraction of work does A complete in 5 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/15. In 5 days, work done = 5/15.
Q7
Medium
A can complete a task in 13 days. After working alone for 4 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 13 days total, remaining days after 4 days = 13 - 4 = 9.
Q8
Medium
A finishes a job in 9 days and B in 18 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/9 + 1/18. Time = 162/27 = 6 days.
Q9
Medium
A can complete a task in 12 days. After working alone for 3 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 12 days total, remaining days after 3 days = 12 - 3 = 9.
Q10
Medium
A finishes a job in 8 days and B in 24 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/8 + 1/24. Time = 192/32 = 6 days.
Q11
Medium
A can complete a task in 14 days. After working alone for 3 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 14 days total, remaining days after 3 days = 14 - 3 = 11.
Q12
Medium
A finishes a job in 10 days and B in 15 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/10 + 1/15. Time = 150/25 = 6 days.
Q13
Medium
A can complete a task in 12 days. After working alone for 4 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 12 days total, remaining days after 4 days = 12 - 4 = 8.
Q14
Medium
A can finish a work in 9 days. What fraction of work does A complete in 6 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/9. In 6 days, work done = 6/9.
Q15
Medium
A can complete a task in 11 days. After working alone for 5 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 11 days total, remaining days after 5 days = 11 - 5 = 6.
Q16
Medium
A can finish a work in 14 days. What fraction of work does A complete in 4 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/14. In 4 days, work done = 4/14.
Q17
Medium
A can complete a task in 13 days. After working alone for 3 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 13 days total, remaining days after 3 days = 13 - 3 = 10.
Q18
Medium
A can finish a work in 12 days. What fraction of work does A complete in 3 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/12. In 3 days, work done = 3/12.
Q19
Medium
A can complete a task in 20 days. After working alone for 9 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 20 days total, remaining days after 9 days = 20 - 9 = 11.
Q20
Medium
A can finish a work in 9 days. What fraction of work does A complete in 4 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/9. In 4 days, work done = 4/9.
Q21
Medium
A can complete a task in 11 days. After working alone for 7 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 11 days total, remaining days after 7 days = 11 - 7 = 4.
Q22
Medium
A finishes a job in 12 days and B in 12 days. In how many days can they finish together?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Combined rate = 1/12 + 1/12. Time = 144/24 = 6 days.
Q23
Medium
A can complete a task in 15 days. After working alone for 3 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 15 days total, remaining days after 3 days = 15 - 3 = 12.
Q24
Medium
A can complete a task in 16 days. After working alone for 10 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 16 days total, remaining days after 10 days = 16 - 10 = 6.
Q25
Medium
A can finish a work in 7 days. What fraction of work does A complete in 4 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/7. In 4 days, work done = 4/7.
Q26
Medium
A can complete a task in 10 days. After working alone for 7 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 10 days total, remaining days after 7 days = 10 - 7 = 3.
Q27
Medium
A can finish a work in 8 days. What fraction of work does A complete in 3 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/8. In 3 days, work done = 3/8.
Q28
Medium
A can complete a task in 12 days. After working alone for 6 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 12 days total, remaining days after 6 days = 12 - 6 = 6.
Q29
Medium
A can finish a work in 13 days. What fraction of work does A complete in 5 days?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. Daily work = 1/13. In 5 days, work done = 5/13.
Q30
Medium
A can complete a task in 14 days. After working alone for 7 days, how many days of work remain?
Explanation:
In work problems, the key is to find each person's work rate (fraction of job per day). Rate = 1 ÷ Days. Add rates when working together. Never add the days directly. If A takes 14 days total, remaining days after 7 days = 14 - 7 = 7.
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
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