Time and Work is an important topic in quantitative aptitude, school mathematics, government exams, banking exams, SSC exams, railway exams, campus placement tests, and many competitive examinations. These questions look simple, but they become confusing when two or more people work together, leave the work, join later, or when pipes fill and empty a tank at the same time.
The main idea of time and work is very clear: work is treated as one complete unit. If a person completes the whole work in 10 days, then the person completes 1/10 of the work in one day. If two people work together, their one-day work is added. If one pipe fills a tank and another pipe empties it, the filling rate and emptying rate are subtracted.
This updated lesson keeps the existing formulas and images in the post and adds simple explanations, tables, solved examples, shortcuts, pipes and cisterns, efficiency method, wages, alternate day work, practice questions, and FAQs. The goal is to make the topic useful for both beginners and exam preparation.
Meaning of Time and Work
Time and work questions are based on the relation between work, time, and efficiency. Work means the task to be completed. Time means the number of days or hours required. Efficiency means the amount of work done in one day or one hour.
If efficiency increases, time decreases. If efficiency decreases, time increases. This means time and efficiency are inversely proportional. For example, if A is twice as efficient as B, A will take half the time taken by B for the same work.
Important Terms
| Term | Meaning |
|---|---|
| Total work | The complete job, usually taken as 1 unit or LCM units |
| One-day work | Part of work completed in one day |
| Efficiency | Work done per unit time |
| Combined work | Work done by two or more persons together |
| Remaining work | Work left after some part is completed |
Existing Basic Formula
If A can do a piece of work in n days then in 1 day’s work 
If A’s day’s work is 1/n than A can finish the work in n days.
Pipes & cisterns
Inlet- a pipe connected with a tank/cistern that fill it is known as an inlet.
Outlet- a pipe connected with a tank/cistern, emptying it is known as an outlet
1) If a pipe can fill a tank in x hours , then part filled in hour = 
2) If pipe can empty a full tank in y hour than part emptied in 1 hour= 
3) If a pipe can fill a tank in x hours & another pipe can empty the full tank in y hours. Than an opening both the pipe the net part filled/emptied
Where y<x filled in 1 hour = 
Where x>y emptied in 1 hour = 
part.
Core Formulas of Time and Work
| Case | Formula |
|---|---|
| A completes work in n days | A’s 1 day work = 1/n |
| A’s 1 day work is 1/n | A completes work in n days |
| A and B work together | 1 day work = 1/A + 1/B |
| Total work | Time x efficiency |
| Required time | Total work / work done per day |
| Efficiency and time | They are inversely proportional |
LCM Method for Time and Work
The LCM method is one of the easiest ways to solve time and work problems. Instead of taking total work as 1, take total work as the LCM of the given days. This avoids fractions and makes calculation faster.
Example: A can complete a work in 12 days and B can complete the same work in 18 days. Find the time taken by A and B together.
LCM of 12 and 18 is 36. So take total work = 36 units.
A’s efficiency = 36/12 = 3 units per day.
B’s efficiency = 36/18 = 2 units per day.
Together they complete 3 + 2 = 5 units per day.
Time required = 36/5 = 7.2 days.
So A and B together can finish the work in 7 1/5 days.
Fraction Method
The fraction method is also useful when only two workers are involved. If A completes work in x days and B completes work in y days, then together they complete 1/x + 1/y work in one day.
Example: A can do a work in 10 days and B can do it in 15 days. Find the time taken together.
A’s 1 day work = 1/10.
B’s 1 day work = 1/15.
Together one-day work = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6.
Therefore they complete the work in 6 days.
Efficiency Ratio and Time Ratio
Efficiency ratio and time ratio are opposite to each other. If two persons do the same work, the one who takes less time has more efficiency.
If A and B take time in the ratio 3:4, then their efficiency ratio is 4:3.
If A is twice as efficient as B, then A takes half the time of B.
Example: A is three times as efficient as B. If B completes a work in 24 days, how many days will A take?
A is 3 times as efficient, so A takes 1/3 of B’s time.
A’s time = 24/3 = 8 days.
Work Done in Some Days
Sometimes the question asks how much work is completed in a fixed number of days. First find one-day work, then multiply by the number of days.
Example: A can finish work in 20 days. How much work will A complete in 5 days?
A’s one-day work = 1/20.
Work in 5 days = 5/20 = 1/4.
So one-fourth of the work is completed and three-fourths of the work remains.
Remaining Work Questions
In many questions, one person works for some days and another person completes the remaining work. The best method is to calculate work completed first, subtract it from total work, and then find the time for remaining work.
Example: A can complete a work in 15 days. A works for 5 days, then B completes the remaining work in 8 days. Find how many days B alone will take to complete the whole work.
A’s 1 day work = 1/15.
A’s work in 5 days = 5/15 = 1/3.
Remaining work = 1 – 1/3 = 2/3.
B completes 2/3 work in 8 days.
B completes 1 work in 8 x 3/2 = 12 days.
Men, Days and Work Formula
When the number of workers changes, use the idea that total work = men x days x efficiency. If efficiency is same, then men x days remains constant for the same work.
Formula:
M1 x D1 = M2 x D2, when efficiency and work are same.
If efficiency is also different, use:
M1 x D1 x E1 = M2 x D2 x E2.
Example: 8 men can complete a work in 15 days. How many days will 12 men take?
8 x 15 = 12 x D.
D = 120/12 = 10 days.
Men, Women and Children Work
Some aptitude questions compare the efficiency of men, women, and children. Convert every worker type into one common unit using the given ratio.
Example: 1 man can do the work of 2 women. If 6 men and 4 women work together, how many women-equivalent workers are there?
1 man = 2 women.
6 men = 12 women.
Total = 12 women + 4 women = 16 women-equivalent workers.
After conversion, use the usual men-days formula.
Wages Based on Work
Wages are divided according to work done, not according to time only. If workers have different efficiencies, divide money in the ratio of their work.
Example: A can finish work in 10 days and B can finish it in 15 days. They complete the work together and receive Rs. 5000. Find A’s share and B’s share.
A’s efficiency = 1/10.
B’s efficiency = 1/15.
Efficiency ratio = 3:2.
So wages are divided in the ratio 3:2.
A’s share = 5000 x 3/5 = Rs. 3000.
B’s share = 5000 x 2/5 = Rs. 2000.
Alternate Day Work
In alternate day questions, people work on different days. Calculate work done in one cycle and then complete the remaining part.
Example: A can do a work in 12 days and B can do it in 18 days. They work on alternate days starting with A. Find the total time.
LCM of 12 and 18 is 36. A’s efficiency = 3 units/day and B’s efficiency = 2 units/day.
In 2 days, they complete 3 + 2 = 5 units.
In 14 days, or 7 cycles, they complete 35 units.
Remaining work = 1 unit.
Next day is A’s turn, and A can do 3 units in one day. Time for 1 unit = 1/3 day.
Total time = 14 1/3 days.
Work and Time with Negative Work
Negative work appears in leakage, wastage, or pipe outlet questions. A filling pipe adds work and an emptying pipe removes work. The net work per hour is the difference between filling rate and emptying rate.
Example: A pipe can fill a tank in 6 hours and a leak can empty it in 12 hours. If both are open, when will the tank be full?
Filling rate = 1/6 tank per hour.
Leak rate = 1/12 tank per hour.
Net rate = 1/6 – 1/12 = 1/12.
So the tank will be full in 12 hours.
Pipes and Cisterns
Pipes and cisterns are a direct application of time and work. Filling a tank is positive work. Emptying a tank is negative work. If more than one inlet is open, add their rates. If an outlet is also open, subtract its rate.
Example: Pipe A fills a tank in 8 hours and pipe B fills it in 12 hours. How long will both pipes take together?
A’s 1 hour work = 1/8.
B’s 1 hour work = 1/12.
Together = 1/8 + 1/12 = 3/24 + 2/24 = 5/24.
Time = 24/5 = 4.8 hours.
So both pipes fill the tank in 4 hours 48 minutes.
Pipe Filling and Emptying Together
Example: One inlet fills a tank in 5 hours and one outlet empties it in 10 hours. If both are opened together, find the time to fill the tank.
Inlet work = 1/5 per hour.
Outlet work = 1/10 per hour.
Net filling = 1/5 – 1/10 = 1/10.
The tank will be filled in 10 hours.
If the outlet is stronger than the inlet, the tank will not fill. Instead, it will empty. Always compare the rates before writing the final answer.
Common Question Types
| Question type | Best method |
|---|---|
| Two workers together | Add one-day work |
| Worker leaves or joins | Calculate completed and remaining work |
| More workers added | Use men-days formula |
| Efficiency ratio | Use inverse time ratio |
| Wages | Divide according to work done |
| Pipes and leak | Add inlet rate and subtract outlet rate |
Solved Examples
Example 1
A can complete a job in 16 days and B can complete it in 24 days. In how many days can they complete it together?
LCM of 16 and 24 is 48. A’s efficiency = 3 units/day. B’s efficiency = 2 units/day.
Together efficiency = 5 units/day.
Time = 48/5 = 9.6 days.
Example 2
A and B together complete a work in 12 days. A alone completes it in 20 days. Find B’s time.
Together one-day work = 1/12.
A’s one-day work = 1/20.
B’s one-day work = 1/12 – 1/20 = 5/60 – 3/60 = 2/60 = 1/30.
So B alone can complete the work in 30 days.
Example 3
10 men can complete a work in 18 days. After 6 days, 5 more men join. Find total time required.
Total work = 10 x 18 = 180 man-days.
Work done in first 6 days = 10 x 6 = 60 man-days.
Remaining work = 120 man-days.
Now workers = 15.
Remaining time = 120/15 = 8 days.
Total time = 6 + 8 = 14 days.
Example 4
A can do a work in 30 days. B is 50 percent more efficient than A. Find B’s time.
If A’s efficiency is 100, B’s efficiency is 150.
Time ratio A:B = 150:100 = 3:2.
A takes 30 days, so B takes 30 x 2/3 = 20 days.
Example 5
Three pipes A, B, and C can fill a tank in 6, 8, and 12 hours. Find the time taken when all are opened together.
LCM of 6, 8, and 12 is 24.
A fills 4 units/hour, B fills 3 units/hour, C fills 2 units/hour.
Together they fill 9 units/hour.
Time = 24/9 = 8/3 hours = 2 hours 40 minutes.
Example 6
A can finish a work in 10 days and B can finish it in 20 days. They work together for 4 days. How much work remains?
A and B one-day work = 1/10 + 1/20 = 3/20.
Work in 4 days = 4 x 3/20 = 3/5.
Remaining work = 1 – 3/5 = 2/5.
Common Mistakes
- Adding days directly instead of adding one-day work.
- Forgetting that time and efficiency are inverse.
- Dividing wages according to days even when efficiencies are different.
- Not subtracting outlet work in pipe and leak questions.
- Using total work as 1 when LCM method would be faster.
- Ignoring remaining work when someone leaves or joins later.
Practice Questions
- A can complete a work in 25 days. What is A’s one-day work?
- A can complete a work in 15 days and B in 20 days. How long will they take together?
- A and B together finish work in 8 days. A alone takes 12 days. Find B’s time.
- 12 men can complete a work in 10 days. How many days will 15 men take?
- A pipe fills a tank in 9 hours and another fills it in 18 hours. Find time together.
- A pipe fills a tank in 6 hours and a leak empties it in 15 hours. Find net filling time.
- A is twice as efficient as B. If B takes 30 days, find A’s time.
- A and B work together for 5 days and complete half the work. How long will they take to finish the full work together?
Answers to Practice Questions
- 1/25.
- 60/7 days.
- 24 days.
- 8 days.
- 6 hours.
- 10 hours.
- 15 days.
- 10 days.
Frequently Asked Questions
What is the basic formula of time and work?
If a person completes work in n days, then one-day work is 1/n. If one-day work is 1/n, the full work is completed in n days.
How do two people working together finish work faster?
Their one-day work is added. A higher combined rate means less time is needed.
What is efficiency in time and work?
Efficiency means work done per day or per hour. More efficiency means less time for the same work.
How are wages divided in time and work?
Wages are divided according to the amount of work done by each person.
What is the difference between time and work and pipes and cisterns?
Pipes and cisterns use the same concept. Filling is positive work and emptying is negative work.
Which method is best for exams?
The LCM method is usually best because it avoids fractions and makes calculations faster.
Advanced Time and Work Shortcuts
Some questions can be solved faster by comparing total work units. Suppose A finishes work in 18 days and B finishes it in 24 days. The LCM is 72 units. A does 4 units per day and B does 3 units per day. If the question says A works for 6 days and B works for 8 days, work done is 6 x 4 + 8 x 3 = 48 units. Remaining work is 72 – 48 = 24 units.
This unit method is useful because it can handle almost every mixed time and work question. It also avoids long fractions. Whenever the given days are different, take the LCM as total work and convert every person into units per day.
Delayed Joining Questions
In delayed joining questions, one person starts first and another person joins later. First calculate the work completed before the second person joins. Then calculate the remaining work using their combined efficiency.
Example: A can complete work in 20 days and B can complete it in 30 days. A works alone for 5 days. Then B joins A. Find total time required.
LCM of 20 and 30 is 60 units. A’s efficiency = 3 units/day. B’s efficiency = 2 units/day.
A’s work in first 5 days = 5 x 3 = 15 units.
Remaining work = 60 – 15 = 45 units.
Together efficiency = 3 + 2 = 5 units/day.
Time after B joins = 45/5 = 9 days.
Total time = 5 + 9 = 14 days.
Leaving Work Before Completion
Sometimes one worker leaves before the work is completed. In that case, calculate the work done together first. Then calculate remaining work by the person who continues.
Example: A can do a work in 12 days and B in 18 days. They work together for 4 days, then A leaves. How many more days will B take?
Total work = 36 units. A’s efficiency = 3 units/day and B’s efficiency = 2 units/day.
Work done together in 4 days = 4 x 5 = 20 units.
Remaining work = 36 – 20 = 16 units.
B completes 2 units per day, so time = 16/2 = 8 days.
Total time = 4 + 8 = 12 days.
Work Equivalence Method
Work equivalence means replacing one type of worker with another according to the given efficiency relation. This method is common in questions involving men, women, and children.
Example: 2 men can do the work of 3 women. If 6 men and 9 women work together, convert all workers into women.
2 men = 3 women, so 1 man = 1.5 women.
6 men = 9 women.
Total workers = 9 women + 9 women = 18 women-equivalent.
Now the question becomes a normal worker-days question.
One Worker Is More Efficient by a Percent
If A is 25 percent more efficient than B, then A’s efficiency is 125 when B’s efficiency is 100. The time ratio is inverse, so A:B time = 100:125 = 4:5.
Example: B takes 30 days to complete a work. A is 50 percent more efficient than B. Find A’s time.
B’s efficiency = 100 and A’s efficiency = 150.
Time ratio A:B = 100:150 = 2:3.
A’s time = 30 x 2/3 = 20 days.
Pipe Questions with Partly Filled Tank
If the tank is already partly filled, only the remaining part must be filled. If the tank is partly emptying, calculate the net rate and apply it to the remaining part.
Example: A pipe fills a tank in 10 hours. A leak empties a full tank in 20 hours. If the tank is half full and both pipe and leak are open, how long will it take to fill the tank?
Net filling rate = 1/10 – 1/20 = 1/20 tank per hour.
Remaining tank = 1/2.
Time = (1/2) / (1/20) = 10 hours.
Revision Tips for Exams
Read the question carefully and underline who works alone, who works together, and who leaves or joins. If wages are mentioned, find the ratio of work done. If pipes are mentioned, decide which pipes fill and which pipes empty. If efficiency is given as a ratio or percent, convert it before calculation.
For quick solving, remember these points: one-day work is 1/days, total work can be taken as LCM, combined work is the sum of rates, and leakage is negative work. Most time and work questions become straightforward once these four ideas are clear.
Conclusion
Time and Work becomes easy when you think in terms of one-day work and efficiency. Do not add the number of days directly. Convert days into work rate, combine the rates, and then find the required time.
For pipes and cisterns, use the same idea. Add filling rates and subtract emptying rates. With regular practice of LCM method, remaining work, wages, and alternate day examples, this topic becomes one of the scoring areas in aptitude exams.