Master CAT Time And Work
Master CAT time and work questions with one reusable shortcut, the key formulas you actually need, and solved practice questions built for exam speed
Master CAT Time And Work
One clean trick turns messy time and work fractions into a two-line calculation. Here's exactly how it works.
The fastest way to solve CAT time and work questions is to stop working in fractions altogether. Convert every rate into a one-day rate against a shared total, usually the LCM of the given times, and the arithmetic turns into whole-number addition.
You've probably lived this in a mock: two people building a wall, 1/12 plus 1/18, and by the time you find a common denominator, ninety seconds are gone. There's a faster starting point.
Want to test the method now? Try a set of CAT time and work practice questions and see how much faster the one-day unit approach feels.
- Skip fractions. Convert every rate into whole one-day units using the LCM of the given time values.
- Add or subtract one-day rates directly once they share the same total-work base.
- The same rate logic covers people joining midway and pipes-and-cistern questions, where an outlet pipe simply subtracts.
- Test the method against real practice questions before you trust it under time pressure.
Why Do Time and Work Fractions Trip You Up?
Fractions trip you up because CAT rewards speed, and adding unlike fractions under a two-minute limit is where errors creep in. The standard "1 unit of work" method isn't wrong, just slower than it needs to be once a third person enters the picture.
Say two people finish a task in 12 and 18 days alone. The textbook approach makes each daily rate 1/12 and 1/18, so combining them means finding a common denominator, 36, before you can add anything.
The One-Day Unit Trick: Slow Method vs. Fast Method
| Step | Slow Method (Fractions) | Fast Method (One-Day Unit Trick) |
|---|---|---|
| Total work | 1 abstract unit | LCM of 12 and 18 = 36 |
| A's daily rate | 1/12 | 36 ÷ 12 = 3 units/day |
| B's daily rate | 1/18 | 36 ÷ 18 = 2 units/day |
| Combined rate | 1/12 + 1/18 = 5/36 | 3 + 2 = 5 units/day |
| Days together | 36/5 = 7.2 | 36 ÷ 5 = 7.2 |
Picking a random large number as "total work" instead of the actual LCM. Any common multiple works mathematically, but the LCM keeps numbers small enough to calculate in your head.
The One-Day Unit Trick, Step by Step
Three moves, no fractions: find the LCM of every time value, convert each person's time into a one-day rate against that shared total, then add or subtract those rates directly.
If the given times share an obvious common factor, like 10, 15, and 30, the LCM is usually smaller than you'd guess. Check before multiplying everything together.
Put the Trick to Work
Reading about the One-Day Unit Trick and using it under a timer are two different skills.
Start Practicing NowTry a three-person version: A finishes in 10 days, B in 15, C in 30. LCM(10,15,30) = 30 units. A does 3 units a day, B does 2, C does 1, combined rate 6 a day, finishing in 30 ÷ 6, or 5 days, no common denominator anywhere.
Practice this exact setup on CAT time and work previous year questions. For the complete shortcut list, see our Time and Work Formulas for CAT 2026: 18 Shortcuts, 15 PYQs.
How Do You Handle People Joining or Leaving Midway?
The trick handles a mid-way change cleanly: calculate work finished up to that point using the combined rate, then recompute the remaining rate. No restarting from scratch.
Take the three-person example: A, B, C work at 3, 2, 1 units a day in a 30-unit job. If C leaves after 2 days, the trio has completed 2 × 6, or 12 units, leaving 18 undone. From day 3, only A and B remain at 5 units a day, so the rest takes 18 ÷ 5, or 3.6 more days.
This setup sometimes shows up as a DILR caselet instead of a straight quant question. If that version trips you up, see our Time and Work DILR Sets for CAT: 3 Worked Examples.
How Are Pipes and Cisterns Different?
Same rate logic, one twist: an outlet pipe subtracts from the combined rate instead of adding to it. Treat every inlet as positive, every outlet as negative.
A tank is filled by pipe A in 20 hours, drained by outlet B in 30 hours. LCM(20,30) = 60 units. A fills 3 units an hour, B drains 2, net rate 1 unit an hour, so the tank fills in 60 hours, three times slower than without the leak.
If a question mentions a leak or outlet pipe without saying how long it takes to empty the tank alone, that missing value is almost always what the question is asking you to find.
The Bottom Line on Time and Work
Time and work stops being a fraction-juggling exercise the moment you stop treating the job as one abstract unit. LCM first, one-day rates second, direct combination third, and those same three moves carry you through joining, leaving, and pipes-and-cistern variations.
Ready to Test It Under Time Pressure?
The real test of the One-Day Unit Trick is a timer, not a re-read.
Practice Time and Work QuestionsFrequently Asked Questions
What is the LCM method in time and work questions?
It means treating the total work as the LCM of the given time values instead of as an abstract '1 unit of work'. This turns everyone's work rate into a whole number, which is far easier to add and subtract under time pressure.
How do I handle time and work questions where people join or leave midway?
The One-Day Unit Trick handles this cleanly: calculate the work completed up to the change using the combined one-day rate, then recompute the remaining rate for the time that follows.
Are time and work and pipes and cistern questions solved the same way?
Yes, the underlying rate logic is identical. The only real difference is that an outlet pipe subtracts from the combined rate instead of adding to it.
How many time and work questions typically appear in CAT quant?
It varies by year and slot, but the topic shows up consistently as part of CAT's arithmetic question cluster, so it is worth mastering rather than skipping.
This guide was built by reviewing recurring time and work question patterns across recent CAT papers and testing the One-Day Unit Trick against the standard fraction method for speed and accuracy.
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