Time and Work Questions with Step-by-Step Solutions
One method covers most questions: find each worker's daily work, then add or subtract.
Time and work questions ask how long a job takes when people, machines or pipes work at different speeds. Most of them are solved by the same idea: find how much work each worker does in one day, then add or subtract.
This page shows that one method, then uses it on six original practice questions. Each solution is written step by step so you can follow it without a shortcut you do not understand.
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The Question Types You Will Meet
All of these use the same one-day-work idea.
- Working together
- Two or more people work at the same time. Add their one-day work.
- Finding one person's time
- You know the pair's time and one person's time. Subtract to get the other person.
- Efficiency
- "A is twice as efficient as B" means A does twice B's work in a day, so A needs half B's time.
- Leaving or joining midway
- Work done in the first stretch is subtracted from the total; the rest is finished at the new rate.
- Work and wages
- Pay is shared in the ratio of work done, not the ratio of days taken.
- Pipes and cisterns
- Filling pipes add work; an emptying pipe (a leak or outlet) subtracts it.
The Method: Total Work as an LCM
Fractions slow you down. Treat the job as a number of units instead.
- 1
Take the LCM of all the days given
Call this the total work. If A takes 12 days and B takes 18 days, the LCM is 36, so the job is 36 units.
- 2
Find each worker's one-day work
Divide the total by that worker's days. A does 36 ÷ 12 = 3 units a day; B does 36 ÷ 18 = 2 units a day.
- 3
Combine the rates
Add rates for people working together. Subtract the rate of anything that undoes work, such as an outlet pipe.
- 4
Divide total work by the combined rate
Time = total work ÷ work per day. Then check the answer is sensible: together must be faster than the fastest worker alone.
Practice Questions with Full Solutions
Try each one before reading the solution.
- 1
Practice question 1: A can finish a job in 12 days and B in 18 days. How long will they take together?
Total work = LCM(12, 18) = 36 units. A does 3 units a day, B does 2. Together they do 5 units a day. Time = 36 ÷ 5 = 7.2 days, or 7 1/5 days. Check: this is less than 12, A's time alone, so it makes sense.
- 2
Practice question 2: A and B together finish a job in 10 days. A alone takes 15 days. How long does B take alone?
Total work = LCM(10, 15) = 30 units. A and B together do 30 ÷ 10 = 3 units a day. A alone does 30 ÷ 15 = 2 units a day. So B does 3 − 2 = 1 unit a day, and needs 30 ÷ 1 = 30 days.
- 3
Practice question 3: A is twice as efficient as B. Working together, they finish a job in 14 days. How long would A take alone?
Let B do 1 unit a day, so A does 2. Together: 3 units a day. Total work = 3 × 14 = 42 units. A alone needs 42 ÷ 2 = 21 days. (B alone would need 42 days, which matches "half the time" for A.)
- 4
Practice question 4: A can do a job in 20 days and B in 30 days. They work together for 6 days, then A leaves. How many more days does B need?
Total work = LCM(20, 30) = 60 units. A does 3 a day, B does 2. In 6 days together they do 6 × 5 = 30 units. Remaining work = 60 − 30 = 30 units. B alone needs 30 ÷ 2 = 15 more days.
- 5
Practice question 5: A can finish a job in 8 days and B in 12 days. They do it together and are paid ₹3,000. What is A's share?
Total work = LCM(8, 12) = 24 units. A does 3 a day, B does 2. They work the same number of days, so the work done is in the ratio 3 : 2. A's share = 3/5 × ₹3,000 = ₹1,800. B gets ₹1,200.
- 6
Practice question 6: Pipe P fills a tank in 6 hours and pipe Q in 8 hours. Outlet R empties the full tank in 12 hours. If all three are opened together, how long does the tank take to fill?
Tank = LCM(6, 8, 12) = 24 units. P adds 4 an hour, Q adds 3, R removes 2. Net = 4 + 3 − 2 = 5 units an hour. Time = 24 ÷ 5 = 4.8 hours, which is 4 hours 48 minutes.
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Common Traps
- check_circleAdding days instead of rates. A in 12 days and B in 18 days does not mean 30 days together. Always add one-day work.
- check_circleReading efficiency the wrong way round. Twice as efficient means half the time, not double.
- check_circleForgetting the minus sign for an outlet or leak. It removes work, so subtract its rate.
- check_circleSplitting wages by days. If both work the same days, wages follow the ratio of daily work, not of the days each would take alone.
How IBPS PO Tests Time and Work
The IBPS PO syllabus lists Time & Work under Arithmetic, alongside percentage, ratio, profit and loss, and time, speed and distance. In prelims it belongs to the Quantitative Aptitude section (35 questions, 30 marks). In mains the matching section is Data Analysis & Interpretation (40 questions, 60 marks).
Questions are multiple choice: a short word problem with one numerical answer. The sense check in the method above also helps you rule out wrong options quickly.
FAQs
What is the easiest method for time and work questions?expand_more
Take the LCM of the given days as the total work, find each worker's work per day, combine the rates, and divide the total work by the combined rate. It avoids fractions entirely.
How do you solve time and work questions with efficiency?expand_more
Turn the efficiency into a daily rate. If A is twice as efficient as B, give B 1 unit a day and A 2 units, find the total work from the given time, then divide by the rate you need.
How are wages divided in time and work questions?expand_more
In the ratio of work done. When everyone works the same number of days, that is the ratio of their daily work.
Next steps
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