CAT Quant · Study & Practice

Time & Work

AreaArithmetic DifficultyModerate CAT weightage1–3 questions (directly + inside Pipes & Cisterns, Ratio and word-problem sets)

Time & Work is the chapter where most CAT aspirants quietly lose marks — not because it is hard, but because they solve it the school way, juggling fractions like 1/12 + 1/15. The CAT-smart approach throws fractions out entirely. Set the total work equal to the LCM of all the days given; now each person’s one-day output (their efficiency) is a clean whole number of "units", and the whole problem becomes simple addition and division. If A finishes a job in 12 days and B in 15, take total work = LCM(12,15) = 60 units; A does 5 units/day, B does 4, together 9 units/day, so they finish in 60/9 days. No fractions, no errors, and you can read off "who does how much" instantly. This chapter builds that fluency across five families: individual efficiency, combined work, alternate-day working, work equivalence (the man-days idea), and the M1D1H1/W1 = M2D2H2/W2 master formula for men-women-children mixes. Pipes & Cisterns is the same machinery with inflow positive and leaks negative, so this chapter is your foundation for that topic too. Each section gives the fast method, worked CAT-style examples, and the traps that cost careless students a percentile.

Topics

1 Individual Efficiency 4 worked · 5 practice · 8-Q test Start → 2 Combined Work 4 worked · 5 practice · 8-Q test Start → 3 Alternate Working 4 worked · 5 practice · 8-Q test Start → 4 Work Equivalence 4 worked · 5 practice · 8-Q test Start → 5 Men-Women-Children 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Set total work = LCM of all given days. Each worker’s units/day becomes a clean integer — no fraction addition.
  • Two workers: together time = ab/(a+b). Three or more: just sum the unit-rates and divide.
  • Efficiency is inversely proportional to time. "A is 25% more efficient" ⇒ efficiency 5:4 ⇒ time 4:5.
  • Alternate days: make a 2-day cycle, count whole cycles, then finish the remainder day-by-day (mind who starts).
  • Man-days: men × days (× hours) is constant for the same job — use it for leave/join and hours-change problems.
  • Mixed crews: convert men/women/children to one common unit first, then it is an ordinary man-days problem.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Adding days instead of rates — 12-day and 18-day workers do NOT finish in 30 (or 15) days together.
  • Assuming alternate-day work ends exactly on a cycle boundary; it usually finishes mid-cycle.
  • Forgetting that more workers means fewer days — treating man-days as a direct ratio instead of an inverse one.
  • In mixed-workforce sums, adding men and women without converting to a common efficiency unit.
  • Splitting wages equally instead of in the ratio of work actually done (efficiency × days worked).

📈 CAT exam insight & PYQ analysis

In CAT, pure Time & Work questions have thinned out, but the underlying machinery is everywhere — Pipes & Cisterns (a direct relabelling with negative rates for leaks), ratio-based work-share problems, and word-problem sets that bury a work rate inside a larger story. The recurring patterns are: combined work with a worker joining or leaving partway, alternate-day cycles, and man-day equivalence with changing workforce or hours. XAT and SNAP lean a little more on classic men-women-children mixes. Prioritise the LCM-unit method and efficiency ratios; these turn two-minute fraction grinds into 30-second mental solves, which is exactly where the percentile is won.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Fast way to set total work?Tap to reveal
Total work = LCM of all given days
Combined time for two workers (a, b days)?Tap to reveal
ab/(a+b) days
Efficiency vs time relationship?Tap to reveal
Inversely proportional (efficiency ∝ 1/time)
A is 50% more efficient than B ⇒ time ratio A : B?Tap to reveal
2 : 3
Man-days rule for the same job?Tap to reveal
M1 × D1 = M2 × D2
Full chained work formula?Tap to reveal
M1·D1·H1 / W1 = M2·D2·H2 / W2
Alternate-day cycle length for two workers?Tap to reveal
2 days (one turn each)
How are wages split?Tap to reveal
In the ratio of work done (efficiency × days worked)
A (12 d) and B (18 d) together take?Tap to reveal
LCM 36; rates 3+2=5 ⇒ 36/5 = 7.2 days
Leak in a tank contributes what kind of rate?Tap to reveal
A negative rate (subtract it)
10 men finish in 6 days = how many man-days?Tap to reveal
60 man-days
Before adding men + women, you must…?Tap to reveal
Convert both to one common efficiency unit

📌 Quick revision

Time & Work is fastest when you ditch fractions: set total work = LCM of the days, turn each person’s time into whole units/day (efficiency), then add rates for combined work and divide. Remember efficiency ∝ 1/time and the two-worker shortcut ab/(a+b). For alternate days, build a 2-day cycle and finish the remainder carefully. Man-days (M1·D1 = M2·D2, extended to hours) handles workforce and hour changes — it is an inverse relationship, so more workers means fewer days. For men-women-children, convert everyone to one unit before applying M1·D1·H1/W1 = M2·D2·H2/W2. Split wages by work done, never equally, and treat leaks as negative work.

Chapter test

📝 Time & Work — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered Time & Work when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (5 topics)5/5
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards