Time, Work, Pipes and Productivity Previous Year Questions (PYQs) for CAT: 13+ Solved Questions with Step-by-Step Solutions

Solve 13+ Time, Work, Pipes and Productivity previous year questions for CAT with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Time, Work, Pipes and Productivity

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Chapter Journey

Time, Work, Pipes and Productivity

Step 1 • 11 CAT PYQs • Importance 0.75

👷 Work Rates and Efficiency

Master work units, rates, efficiency ratios, groups, partial work, and replacement logic.

Step 2 • 3 CAT PYQs • Importance 0.35

🔁 Alternating Work and Rosters

Handle day-wise cycles, alternate-day work, rotating pairs, and leftover work.

Step 3 • 3 CAT PYQs • Importance 0.35

💰 Payments, Wages and Cost Optimization

Split wages by work done and choose efficient worker combinations under cost constraints.

Step 4 • 3 CAT PYQs • Importance 0.35

🚰 Pipes, Tanks and Drains

Convert filling and emptying into positive and negative work rates.

By the end of this chapter: you should be able to convert every worker, pipe, or team into a rate and add their contributions cleanly.

Work Rates and Efficiency

Arithmetic → Time, Work, Pipes and Productivity → Topic 1

Work Rates and Efficiency

The whole topic is one idea: work completed equals rate multiplied by time.

R×T

Work rate

Efficiency ratios

Man-hours

Team productivity

Time, Work, Pipes and Productivity: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Quantitative Ability NAT

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

Correct Answer:

Step-by-Step Solution

This is a man-hours with different hourly rates work problem. Recognise it because Renu and Seema have different individual rates of work per hour, and the question links their working hours per day and number of days together with ratios ("double the hours", "double the days") rather than giving them directly.

Step 1 — find each person's rate of work per hour.

Renu completes the task in 15 days at 4 hours/day, so her total work-hours for the whole task are $15 \times 4 = 60$ hours. Her rate is:

$Renu’s rate = \frac{1 task}{60 hours} = \frac{1}{60} task/hour$

Seema completes the task in 8 days at 5 hours/day, so her total work-hours are $8 \times 5 = 40$ hours. Her rate is:

$Seema’s rate = \frac{1}{40} task/hour$

Step 2 — set up the joint working conditions.

Renu works 2 hours/day (given). Seema works double the hours per day as Renu:

$Seema’s hours/day = 2 \times 2 = 4 hours/day$

Let Seema work $d$ days. Renu works double the number of days as Seema:

$Renu’s days = 2 d$

Step 3 — write each person's total work contribution.

$Renu’s work = rate \times hours/day \times days = \frac{1}{60} \times 2 \times 2 d = \frac{4 d}{60} = \frac{d}{15}$

$Seema’s work = \frac{1}{40} \times 4 \times d = \frac{4 d}{40} = \frac{d}{10}$

Step 4 — total work equals 1 completed task.

$\frac{d}{15} + \frac{d}{10} = 1$

Using LCM 30:

$\frac{2 d}{30} + \frac{3 d}{30} = 1 ⟹ \frac{5 d}{30} = 1 ⟹ \frac{d}{6} = 1 ⟹ d = 6$

Step 5 — verify.

Seema works $d = 6$ days at 4 hours/day = 24 hours total; her work $= 24/40 = 0.6$ . Renu works $2 d = 12$ days at 2 hours/day = 24 hours total; her work $= 24/60 = 0.4$ . Sum $= 0.6 + 0.4 = 1.0$ ✓ — the task is exactly completed.

Trap: it's tempting to assume "double the hours" and "double the days" both apply to the same person's baseline, but they actually cross-reference each other (Seema's hours depend on Renu, Renu's days depend on Seema) — read each relationship carefully and assign the variable to the quantity given directly (Seema's days, since Renu's days is derived from it).

The final answer is 6 days.

Question 2 · Quantitative Ability NAT

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

Correct Answer:

Step-by-Step Solution

This is a work rates in harmonic progression problem — recognisable because the question explicitly says the daily work amounts are in HP, and separately gives a time relationship plus partial-work data to find someone's solo time.

Step 1: Understand what HP of rates means.

Let Amal, Sunil, Kamal's daily work rates be $a$ , $s$ , $k$ (job done per day). "Rates in HP" means their reciprocals $\frac{1}{a}, \frac{1}{s}, \frac{1}{k}$ are in AP (arithmetic progression) — this is the definition of HP.

Step 2: Use "Kamal takes twice as much time as Amal".

Time is the reciprocal of rate, so:

$\frac{1}{k} = 2 \times \frac{1}{a} ⟹ k = \frac{a}{2}$

Step 3: Apply the AP condition to find $s$ .

Since $\frac{1}{a}, \frac{1}{s}, \frac{1}{k}$ are in AP:

$\frac{2}{s} = \frac{1}{a} + \frac{1}{k} = \frac{1}{a} + \frac{2}{a} = \frac{3}{a}$

$\frac{1}{s} = \frac{3}{2 a} ⟹ s = \frac{2 a}{3}$

Step 4: Compute the total work done from the given days.

$Amal’s contribution = 4 a$

$Sunil’s contribution = 9 s = 9 \times \frac{2 a}{3} = 6 a$

$Kamal’s contribution (remaining work) = 16 k = 16 \times \frac{a}{2} = 8 a$

Total work:

$W = 4 a + 6 a + 8 a = 18 a$

Step 5: Find the number of days Sunil alone needs.

$Days = \frac{W}{s} = \frac{18 a}{\frac{2 a}{3}} = 18 a \times \frac{3}{2 a} = 27$

Answer: 27 days.

Common trap: applying the HP condition directly to the rates $a, s, k$ as if they were in AP (instead of their reciprocals) — this changes the relationship between $a$ , $s$ , and $k$ and leads to a wrong value of $s$ .

Question 3 · Quantitative Ability NAT

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

Correct Answer:

Step-by-Step Solution

Key idea: this is a pair-rate work problem, recognisable because the completion times of three pairs of workers are given and an individual time is asked.

Step 1: Convert all times to months.

$1 year = 12 months, 2 years = 24 months .$

Step 2: Let Amar's rate be $a$ , Akbar's rate be $b$ , and Anthony's rate be $c$ , measured as project fraction per month.

Step 3: Translate the given pair times into rates:

$a + b = \frac{1}{12},$

$b + c = \frac{1}{16},$

$c + a = \frac{1}{24} .$

Step 4: Add all three equations:

$2 (a + b + c) = \frac{1}{12} + \frac{1}{16} + \frac{1}{24} .$

Step 5: Compute the sum:

$\frac{1}{12} + \frac{1}{16} + \frac{1}{24} = \frac{4 + 3 + 2}{48} = \frac{9}{48} = \frac{3}{16} .$

So:

$2 (a + b + c) = \frac{3}{16}$

$a + b + c = \frac{3}{32} .$

Step 6: Find individual rates by subtracting the opposite pair rate.

Amar:

$a = (a + b + c) - (b + c) = \frac{3}{32} - \frac{1}{16} = \frac{3}{32} - \frac{2}{32} = \frac{1}{32} .$

Akbar:

$b = (a + b + c) - (c + a) = \frac{3}{32} - \frac{1}{24} = \frac{9}{96} - \frac{4}{96} = \frac{5}{96} .$

Anthony:

$c = (a + b + c) - (a + b) = \frac{3}{32} - \frac{1}{12} = \frac{9}{96} - \frac{8}{96} = \frac{1}{96} .$

Step 7: Convert rates to times:

Amar takes $32$ months, Akbar takes $\frac{96}{5} = 19.2$ months, Anthony takes $96$ months.

Step 8: The fastest is Akbar, the slowest is Anthony, so the person neither fastest nor slowest is Amar.

Answer: $32$ months.

Question 4 · Quantitative Ability NAT

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is

Correct Answer:

340

Step-by-Step Solution

Key idea: this is an efficiency-ratio work question, recognisable because workers are described as multiples of each other's efficiency and one worker leaves during the job.

Step 1: Let Chandan's work rate be $c$ job per day.

Step 2: Bipin is twice as efficient as Chandan, so Bipin's rate is:

$2 c .$

Step 3: Ankita is twice as efficient as Bipin, so Ankita's rate is:

$2 (2 c) = 4 c .$

Step 4: All three start together. Their combined rate for the first 20 days is:

$4 c + 2 c + c = 7 c .$

Step 5: Work done in the first 20 days:

$20 \times 7 c = 140 c .$

Step 6: Bipin leaves after 20 days. The job is completed in 60 days, so the remaining time is:

$60 - 20 = 40 days .$

Step 7: For the remaining 40 days, only Ankita and Chandan work. Their combined rate is:

$4 c + c = 5 c .$

Step 8: Work done in the remaining 40 days:

$40 \times 5 c = 200 c .$

Step 9: Total work:

$140 c + 200 c = 340 c .$

Step 10: Chandan alone works at rate $c$ , so time taken by Chandan alone is:

$\frac{340 c}{c} = 340 days .$

Answer: $340$ .

Question 5 · Quantitative Ability NAT

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

Correct Answer:

Step-by-Step Solution

Key idea: This is a compensation condition reveals rate ratio question, recognisable because one worker reducing output forces the other to increase output to maintain the same combined rate.

Why this method: The combined daily output must stay the same. The compensation condition gives a second equation linking the two rates, letting us find each rate individually.

Step-by-step working:

Define rates:

Let Gautam's daily rate = $g$ , Suhani's daily rate = $s$
Together: $g + s = \frac{1}{20}$ ... (1)

Apply the compensation condition:

Gautam at 60% + Suhani at 150% = same total output
$0.6 g + 1.5 s = g + s$
$0.5 s = 0.4 g$
$\frac{g}{s} = \frac{5}{4}$ ... (2)

Solve for individual rates:

From (2): $g = \frac{5}{4} s$
Substitute into (1): $\frac{5}{4} s + s = \frac{1}{20}$
$\frac{9}{4} s = \frac{1}{20}$
$s = \frac{4}{180} = \frac{1}{45}$
$g = \frac{5}{4} \times \frac{1}{45} = \frac{1}{36}$

Find time for each worker alone:

Gautam alone: $\frac{1}{g} = 36$ days
Suhani alone: $\frac{1}{s} = 45$ days

Identify the faster worker:

Gautam (36 days) is faster than Suhani (45 days)

Answer: The faster worker (Gautam) takes 36 days to complete the job alone.

Time, Work, Pipes and Productivity Previous Year Questions (PYQs) for CAT: 13+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Time, Work, Pipes and Productivity

Time, Work, Pipes and Productivity

👷 Work Rates and Efficiency

🔁 Alternating Work and Rosters

💰 Payments, Wages and Cost Optimization

🚰 Pipes, Tanks and Drains

Work Rates and Efficiency

Work Rates and Efficiency

Time, Work, Pipes and Productivity: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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