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Time & Work for CAT: Formulas, Weightage & Question Types

Work as a rate: combinations, people joining and leaving, pipes and rosters.

Time & Work formula sheet

Everything CAT needs from Time & Work, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. aa and bb are the days each person needs alone.

The one idea

Raterate=worktime\text{rate} = \dfrac{\text{work}}{\text{time}}
A's rate, if A alone takes aa days1a\dfrac{1}{a} of the job per day
Working together1a+1b\dfrac{1}{a} + \dfrac{1}{b}
Days together, two peopleaba+b\dfrac{ab}{a+b}
Days together, three people11a+1b+1c\dfrac{1}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}
Work donerate×days worked\text{rate} \times \text{days worked}

Rates add. Times never do. Everything below is a consequence.

Efficiency and ratios

Efficiency∝1time\propto \dfrac{1}{\text{time}}
Times in ratio a:ba : brates are in ratio b:ab : a
"xx is twice as fast as yy"ratex=2 ratey\text{rate}_x = 2\,\text{rate}_y, so xx takes half the time
"xx needs 25% more time than yy"tx=1.25 tyt_x = 1.25\,t_y, so ratex=0.8 ratey\text{rate}_x = 0.8\,\text{rate}_y

Pipes

Filling pipepositive rate
Draining pipenegative rate
Netadd them, signs included
Tank fills only ifthe net rate is positive

Man-days — when people, days and hours all move

Work ∝\propto people ×\times days ×\times hours/dayM1D1H1W1=M2D2H2W2\dfrac{M_1 D_1 H_1}{W_1} = \dfrac{M_2 D_2 H_2}{W_2}
One person's output per hourteam’s workpeople×hours\dfrac{\text{team's work}}{\text{people} \times \text{hours}}

Wages

Share of the money∝\propto work actually done, not days present
Work done by one persontheir rate×days they worked\text{their rate} \times \text{days they worked}
So the shares arein the ratio of those products

Harmonic and arithmetic

Rates in HPthe times are in AP
Rates in APthe times are in HP

The 6 Time & Work question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine. Beyond these, CAT has asked 7 rarer one-off shapes here.

  1. 01

    You are given combinations, never individuals

  2. 02

    Somebody joins or leaves partway

  3. 03

    Pipes, with one working against you

  4. 04

    People, days and hours all moving

  5. 05

    Split the money

  6. 06

    A repeating roster

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Time & Work in CAT: quick answers

How many Time & Work questions come in CAT Quant?
About 1.3 questions in a 22-question Quant section, worth roughly 4 marks. Time & Work appeared in 22 of the 24 CAT papers from 2017 to 2025, 35 questions in all, which ranks it 3 of 25 Quant chapters.
Are Time & Work questions in CAT MCQ or TITA?
46% of the Time & Work questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Time & Work questions does CAT ask?
CAT keeps returning to 6 question shapes in Time & Work: You are given combinations, never individuals; Somebody joins or leaves partway; Pipes, with one working against you; People, days and hours all moving; Split the money; A repeating roster.

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