Time and Work Formulas for CAT 2026: 18 Shortcuts + 15 PYQs
Time and work formulas for CAT 2026 are one of the most consistently tested Arithmetic sub-topics alongside Percentages and TSD. The reason CAT keeps returning to this topic is structural: it tests rate-of-work logic that maps cleanly to multi-step word problems, and the efficiency method shortcut separates a 2-minute solve from a 5-minute solve. This cheatsheet pins 18 shortcuts across four recognition blocks, then closes with 15 CAT-level PYQs that mirror the patterns setters reuse year after year.
The reason most online time and work content underperforms is that it leads with the 1/a + 1/b fraction method as the primary tool. CAT 2026 will test alternate-day patterns, three-worker chains with one leaving partway, pipes-and-cisterns with outlet pipes, and wages split where the fraction method gets messy fast. The 18 shortcuts below lead with the efficiency method instead, because it scales to every CAT variant without changes.
Why the Efficiency Method Is the Hero of CAT Time and Work
The efficiency method treats total work as a unit count and each worker as a rate. Setting total work as the LCM of individual times means every worker's daily output is an integer. Two workers, three workers, alternate days, outlet pipes, one worker leaving partway, and wages problems all reduce to integer arithmetic in the efficiency framework. The 1/a + 1/b fraction method works only on the simplest two-worker question. The efficiency method works on everything CAT setters can throw at the topic.
The split between school-level and CAT-level time and work content is exactly here. School textbooks teach fraction-first. CAT 2026 questions almost always have a twist that breaks fraction-first thinking, which is why this blog leads with efficiency and treats the fraction method as a backup.
The 18 Time and Work Formulas for CAT 2026
The cheatsheet groups all 18 time and work formulas for CAT 2026 into four blocks. Each block has a recognition cue describing the question type that triggers it. Working block by block builds the LCM-first habit that the drill depends on.
Block 1 — Basic Time, Work and Efficiency (5 formulas)
The basic block is the entry point. These five identities define the relation between time, work and efficiency. Recognition cue: one or two workers, with no twist on alternate days, outlet pipes, or workers leaving partway.
| # | Formula | Use case |
|---|---|---|
| 1 | Work = Efficiency × Time | Foundation relation. |
| 2 | Efficiency of A = Total Work / Time taken by A | Single-worker rate. |
| 3 | Set Total Work = LCM(individual times) | LCM efficiency method setup. |
| 4 | Time together = Total Work / (sum of efficiencies) | Joint completion time. |
| 5 | 1/Timetogether = 1/a + 1/b (backup form) | Two-worker fraction backup. |
Block 2 — Multi-Worker Chains and Alternate Day Patterns (5 formulas)
The multi-worker block extends to three or more workers and to alternate-day cycles where workers rotate in. CAT setters use this pattern in roughly 1 of 3 time and work questions. Recognition cue: three workers mentioned, alternate days, one worker joins or leaves partway, or a cyclic rotation.
| # | Formula | Recognition cue |
|---|---|---|
| 6 | Three workers together: Time = (abc) / (ab + bc + ca) | Three-person formula form. |
| 7 | Alternate days A then B: work per 2 days = eA + eB; total time depends on cycle | Two-day rotation. |
| 8 | If A leaves after k days: work done by A = eA × k; remaining work = total − eAk | Worker leaves partway. |
| 9 | If B joins after k days: remaining time = (total − eAk) / (eA + eB) | Worker joins partway. |
| 10 | Cycle pattern A, B, C repeating: work per 3 days = eA + eB + eC | Three-day rotation. |
Block 3 — Pipes and Cisterns (4 formulas)
The pipes-and-cisterns block is a structural variant of time and work where outlet pipes are negative-efficiency workers. CAT pipes and cisterns CAT 2026 questions test the alternate-pipe and net-positive-versus-negative patterns. Recognition cue: tank, cistern, fill, empty, leak, or outlet mentioned in the stem.
| # | Formula | Use case |
|---|---|---|
| 11 | Inlet pipe efficiency = +(Total / Fill time); outlet = −(Total / Empty time) | Sign convention for pipes. |
| 12 | Net fill time = Total Work / (sum of signed efficiencies) | Mixed inlet and outlet running together. |
| 13 | Alternate inlet and outlet: net per 2 hours = eA + eB (which may be negative if outlet stronger) | Alternate-pipe pattern. |
| 14 | Leak detected after fill: leak efficiency = original fill rate − observed fill rate | Leak diagnosis problem. |
Block 4 — Wages, Share and Special Variants (4 formulas)
The wages block handles payment-split problems and the men-women-children efficiency variants. Recognition cue: rupees, payment, share, daily wage, or differential rates among worker categories.
| # | Formula | Use case |
|---|---|---|
| 15 | Wage share ratio = ratio of efficiencies (not times) | Two or more workers splitting payment. |
| 16 | Wage share = (eA × days A worked) : (eB × days B worked) | Different workers for different durations. |
| 17 | Men-women equivalence: x M = y W means x × eM = y × eW | Mixed-worker pool problems. |
| 18 | Work-rate scaling: if k workers finish in d days, n workers finish in (k × d) / n days | Direct proportion of workforce. |
Three Time and Work Traps That Recur in CAT Papers
Three traps recur across the time and work formulas for CAT 2026 question set. The first is wage-split by time. When two workers finish a job together, the wage split is in the ratio of their efficiencies, not their times. A worker who takes 10 days has efficiency 1/10 and one who takes 15 days has efficiency 1/15. The wage ratio is 3:2, not 2:3. The second trap is the alternate-day cycle boundary. When work finishes mid-cycle, the last partial day is computed from the remaining work divided by that day's worker's rate, not by averaging.
The third trap is the outlet-pipe sign error. When an outlet pipe runs alongside an inlet pipe, the outlet's efficiency must be subtracted. Aspirants who write the outlet rate as positive get a net fill time that is too short. CAT sets the trap option at exactly this value to catch sign mistakes. Always write the sign explicitly when setting up pipes-and-cisterns problems.
15 Time and Work CAT-Level Questions With Solutions
These 15 questions cover all four blocks of the cheatsheet. Each is tagged with the block and the formula it tests. Drill them under timed conditions, target under 90 seconds per question, and use the cheatsheet only for recall after attempting.
A finishes a job in 10 days and B in 15 days. How many days will they take together?
LCM(10, 15) = 30. Eff A = 3, Eff B = 2. Together = 5/day. Time = 30/5 = 6 days. Answer: 6 days
A and B together finish a job in 8 days. A alone takes 12 days. How long does B alone take?
Together rate = 1/8. A rate = 1/12. B rate = 1/8 − 1/12 = 1/24. So B alone takes 24 days. Answer: 24 days
A, B, C finish a job in 12, 15, 20 days alone. How many days together?
LCM = 60. Effs 5 + 4 + 3 = 12/day. Time = 60/12 = 5 days. Answer: 5 days
A finishes in 10 days, B in 15 days. Working on alternate days starting with A, how long to finish?
LCM = 30. Per 2-day cycle: 3 + 2 = 5 units. After 5 cycles (10 days): 25 units. Day 11: A works, 3 more units, total 28. Day 12: B does 2 more, total 30. Answer: 12 days
A and B start a job. A leaves after 4 days. A alone takes 10 days, B alone takes 15 days. Total time?
LCM = 30. Effs 3 and 2. First 4 days together: 5 × 4 = 20 units. Remaining: 10 units for B alone at 2/day = 5 days. Total = 4 + 5 = 9 days. Answer: 9 days
A starts alone (10 days for whole job). After 3 days, B joins (15 days for whole job alone). Total time?
LCM = 30. A in 3 days: 3 × 3 = 9 units. Remaining = 21 units at 5/day = 4.2 days. Total = 3 + 4.2 = 7.2 days. Answer: 7.2 days
Pipe A fills a tank in 12 hours, Pipe B fills it in 18 hours. Both open together?
LCM = 36. Effs +3 and +2. Together +5. Time = 36/5 = 7.2 hours. Answer: 7.2 hours
Pipe A fills a tank in 10 hours, outlet B empties it in 15 hours. Net time to fill?
LCM = 30. Effs +3 and −2. Net = +1/hour. Time = 30 hours. Answer: 30 hours
Pipe A (fills in 8 hrs) and outlet B (empties in 12 hrs) operate alternately, A starts. Time to fill?
LCM = 24. Effs +3 and −2. Per 2-hour cycle: +1. After 22 hours (11 cycles): 22 / 2 = 11 cycles × 1 = 11 units. Hour 23: A pumps +3, total 14? Recount: after 11 cycles 11 units done. Hour 23 (A): +3 = 14 units (not yet 24). Continuing... actually after 21 cycles (42 hours): 21 units, hour 43 (A): +3 = 24. Answer: 43 hours
Without a leak, a tank fills in 8 hours. With a leak, it fills in 10 hours. How long for the leak alone to empty a full tank?
LCM(8, 10) = 40. Fill rate 5/hr, observed 4/hr. Leak rate = 1/hr emptying. Empty time = 40 hours. Answer: 40 hours
A finishes a job in 8 days, B in 12 days. Together they finish a contract for 1000. A's share?
LCM = 24. Effs 3 and 2. Wage ratio 3:2. A gets 1000 × 3/5 = 600. Answer: 600
A works for 4 days alone (10-day rate) then B finishes in 6 days alone (15-day rate). Split a 750 payment.
LCM = 30. Effs 3 and 2. Work A = 12 units, work B = 12 units. Split is 12:12 = 1:1. Each gets 375. Answer: 375 each
2 men or 3 women finish a job in 24 days. How long do 3 men and 6 women take together?
2 M = 3 W means M : W = 3 : 2. Total work (in W-units) = 3 W × 24 = 72. Group rate = 3 M + 6 W = 9 W + 6 W = 15 W effs (since 1 M = 1.5 W, so 3 M = 4.5 W, total 4.5 + 6 = 10.5 W effs). Time = 72 / 10.5 ≈ 6.86 days. Answer: ~6.86 days
12 workers finish a project in 30 days. How many days do 18 workers take?
12 × 30 = 18 × t, so t = 20 days. Answer: 20 days
A and B together finish in 6 days. B and C together finish in 8 days. C and A together finish in 12 days. Days for all three together?
2(a + b + c) = 1/6 + 1/8 + 1/12 = 4/24 + 3/24 + 2/24 = 9/24 = 3/8. So a + b + c = 3/16. Together time = 16/3 days ≈ 5.33. Answer: 16/3 days
Slot Time and Work Into Your CAT 2026 Arithmetic Plan
Time and Work is the third topic in the Arithmetic cluster sequence and benefits the most from being scheduled right after Percentages and Profit Loss. A diagnostic-driven plan slots this block in week three so the cluster compounds.
Slot My Efficiency Method DrillWhere Time and Work Fits in the CAT 2026 Arithmetic Cluster
Time and Work is the third topic in the Arithmetic sequence: Percentages first, then Profit Loss and Discount, then Time and Work. The sequencing matters because the efficiency method draws on ratio thinking, which percentages installs. A focused 3 to 4 day study block in week three of any 9-month CAT plan covers the topic. The block scales to 6 to 8 days for working professionals with limited weekly study hours, still placing the topic in month one.
The Optima Learn CAT exam guide sequences the rest of the Arithmetic cluster, and the CAT 2026 waitlist details page explains how the diagnostic-driven planner decides which Arithmetic topics each aspirant prioritises based on their starting level.
Three Reflexes That Compress Time and Work Solves to Under 90 Seconds
Once 18 formulas are memorised, three reflexes separate aspirants who finish time-and-work questions in 90 seconds from those who take three minutes. Reflex one: LCM-first. Always set total work as the LCM of all stated times before anything else. Reflex two: sign-explicit for pipes. Write a plus or minus on every pipe efficiency. Never leave the sign implicit. Reflex three: wage by efficiency. Whenever the question splits payment, immediately reach for the efficiency ratio, never the time ratio. These three install through timed drill, and the CAT preparation blogs library has companion cheatsheets on Percentages, TSD, and Profit Loss.
Common Doubts About Time and Work Preparation for CAT 2026
Are pipes and cisterns and time-and-work the same topic?
Yes, structurally. Pipes-and-cisterns is just time-and-work with signed efficiencies for inlets and outlets. The same LCM-based framework solves both. CAT typically asks 1 to 2 questions from the combined pool per paper, with pipes-and-cisterns coming up in about 1 in 3 papers.
Is the three-worker formula worth memorising?
The shortcut form Time = (abc)/(ab+bc+ca) is worth memorising for clean three-worker questions. But for any CAT twist (one leaving, one joining, alternate days), the LCM-efficiency method is faster and less error-prone. Memorise the shortcut for clean cases and use efficiency for everything else.
How tricky are the recent CAT 2024 and CAT 2025 time-and-work questions?
Recent papers lean heavily on alternate-day and worker-leaves-partway patterns. CAT 2024 had a clean three-worker question and CAT 2025 had an alternate-day pipes problem. Both rewarded the LCM-efficiency method over fractions. Drill these two specific patterns more than the standard two-worker pattern.
How do I revise this topic one week before CAT 2026?
A one-week revision plan: day one, re-read the 18-formula cheatsheet. Day two, drill basic and three-worker variants. Day three, drill alternate-day and worker-leaves patterns. Day four, drill pipes-and-cisterns including outlet pipes. Day five, attempt 15 mixed-block PYQs under timed conditions. Day six, review every error and re-attempt. Day seven, scan the cheatsheet for 15 minutes only before the exam.
Final note. Time and work formulas CAT 2026 reduce to 18 shortcuts across four blocks, with the efficiency method as the recurring tool across all four. The topic rewards LCM-first thinking over fraction arithmetic. Drill block by block, build the three reflexes, and the CAT score predictor alongside mocks will track the lift across Time and Work, TSD, and Ratio downstream.
