Previous Year CAT Questions for Arithmetic

1. CAT 2024 QA Slot 1 | Arithmetic - Time & Work CAT Question

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

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2. CAT 2024 QA Slot 2 | Arithmetic - Time & Work CAT Question

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

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3. CAT 2024 QA Slot 3 | Arithmetic - Time & Work CAT Question

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

(a)
1/5
(b)
3/10
(c)
1/20
(d)
3/20

4. CAT 2023 QA Slot 1 | Arithmetic - Time & Work CAT Question

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

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Answer: 27

Video Explanation

Text Explanation :

Let the time taken by A and K to complete a work is x and 2x days respectively.

Work done in a day is the efficiency of a person.

Hence, if efficiencies of A, S and K are in Harmonic Progression, time taken by them to finish a work will be in Arithmetic Progression.

∴ Time taken by S alone is arithmetic mean of time taken by A and K alone.
⇒ Time taken by S alone = (x + 2x)/2 = 1.5x

Using unitary method
⇒ 1 = $\frac{1}{x} \times 4$ + $\frac{1}{1.5 x} \times 9$ + $\frac{1}{2 x} \times 16$

⇒ x = 4 + 6 + 8

⇒ x = 18

∴ S will take 1.5 × 18 = 27 days to finish the job alone.

Hence, 27.

Concept:

Harmonic Progression

Time & Work

5. CAT 2023 QA Slot 2 | Arithmetic - Time & Work CAT Question

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

(a)
60
(b)
90
(c)
75
(d)
120

Answer: Option B

Video Explanation

Text Explanation :

Let time taken by A and C alone to fill the tank is A and C hours respectively.
∴ Time taken B alone = (A - 1) hours.

Case 1: All three can fill the tank in 2 hours.
⇒ $\frac{1}{A}$ - $\frac{1}{A - 1}$ + $\frac{1}{C}$ = $\frac{1}{2}$ ...(1)

Case 2: B works for 1 hour and C works for 5/4 hours.
⇒ - $\frac{1}{A - 1} \times 1$ + $\frac{1}{C} \times \frac{9}{4}$ = 1 ...(2)

(1) × 9/4 - (2)
⇒ $\frac{9}{4 A}$ - $\frac{9}{4 (A - 1)}$ + $\frac{1}{A - 1} \times 1$ = $\frac{9}{8}$ - 1

⇒ $\frac{9}{4 A}$ - $\frac{5}{4 (A - 1)}$ = $\frac{1}{8}$

⇒ $\frac{18}{A}$ - $\frac{10}{(A - 1)}$ = 1

⇒ A(A - 1) = 18(A - 1) - 10A

⇒ A² - A = 8A - 18

⇒ A² - 9A + 18 = 0

⇒ A = 3 or 6 hours.

Since A should be less than 5, hence we accept only A = 3 hours.

Now, from (1), we have
⇒ $\frac{1}{A}$ - $\frac{1}{A - 1}$ + $\frac{1}{C}$ = $\frac{1}{2}$

⇒ $\frac{1}{3}$ - $\frac{1}{2}$ + $\frac{1}{C}$ = $\frac{1}{2}$

⇒ C = 3/2 hours = 90 minutes.

Hence, option (b).

Concept:

Time & Work

6. CAT 2023 QA Slot 3 | Arithmetic - Time & Work CAT Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

(a)
21
(b)
17
(c)
16
(d)
20

7. CAT 2023 QA Slot 3 | Arithmetic - Time & Work CAT Question

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

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8. CAT 2022 QA Slot 2 | Arithmetic - Time & Work CAT Question

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is:

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Answer: 6

Video Explanation

Text Explanation :

Ratio of time taken by Anu, Tanu and Manu is 5 : 8 : 10.
⇒ Ratio of efficiencies of Anu, Tanu and Manu = $\frac{1}{5}$ : $\frac{1}{8}$ : $\frac{1}{10}$ = 8 : 5 : 4
Let their efficiencies be 8x, 5x and 4x respectively per hour.

Total work done by them in 4 days = (8x + 5x + 4x) × 4 × 8 = 17x × 32 = 544x

Now, Anu and Tanu worked by 6 days working 6 hours 40 minute i.e., 6 $\frac{2}{3}$ hours daily.
∴ Worked completed by Anu and Tanu = 13x × 6 × $\frac{20}{3}$ = 520x

⇒ Time taken by Manu to complete the remaining work = $\frac{544 x - 520 x}{4 x}$ = 6 hours.

Hence, 6.

9. CAT 2022 QA Slot 3 | Arithmetic - Time & Work CAT Question

A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

(a)
23
(b)
140
(c)
36
(d)
150

Answer: Option B

Video Explanation

Text Explanation :

Let the efficiency of each person be ‘e’ units/hour.

Given,
35% work is done by N men in 10 days working for 7 hours/day, while
65% work is done by N-10 men in 14 days working for 10 hours/day

⇒ $\frac{N \times 10 \times 7}{0.35}$ = $\frac{(N - 10) \times 14 \times 10}{0.65}$

⇒ $\frac{N \times 7}{7}$ = $\frac{(N - 10) \times 14}{13}$

⇒ N = $\frac{(N - 10) \times 14}{13}$

⇒ 13N = 14N – 140

⇒ N = 140

Hence, option (b).

10. CAT 2022 QA Slot 3 | Arithmetic - Time & Work CAT Question

Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is

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11. CAT 2021 QA Slot 1 | Arithmetic - Time & Work CAT Question

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

(a)
8
(b)
6
(c)
5
(d)
7

12. CAT 2021 QA Slot 1 | Arithmetic - Time & Work CAT Question

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

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13. CAT 2021 QA Slot 2 | Arithmetic - Time & Work CAT Question

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

(a)
9100
(b)
9000
(c)
9150
(d)
9200

14. CAT 2021 QA Slot 2 | Arithmetic - Time & Work CAT Question

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is:

(a)
140
(b)
120
(c)
144
(d)
264

15. CAT 2021 QA Slot 3 | Arithmetic - Time & Work CAT Question

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is:

(a)
10
(b)
12
(c)
12.5
(d)
11.5

16. CAT 2021 QA Slot 3 | Arithmetic - Time & Work CAT Question

Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is

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17. CAT 2020 QA Slot 2 | Arithmetic - Time & Work CAT Question

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

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18. CAT 2020 QA Slot 3 | Arithmetic - Time & Work CAT Question

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

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19. CAT 2019 QA Slot 1 | Arithmetic - Time & Work CAT Question

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

(a)
36
(b)
24
(c)
12
(d)
18

20. CAT 2019 QA Slot 1 | Arithmetic - Time & Work CAT Question

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

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21. CAT 2019 QA Slot 2 | Arithmetic - Time & Work CAT Question

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

(a)
13
(b)
12
(c)
15
(d)
14

22. CAT 2019 QA Slot 2 | Arithmetic - Time & Work CAT Question

John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

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23. CAT 2018 QA Slot 1 | Arithmetic - Time & Work CAT Question

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

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Answer: 10

Video Explanation

Text Explanation :

Let a filling pipe fills the tank at ‘a’ liters per hour and a draining pipe drains at ‘b’ liters per hour.

Work done by 6 filling and 5 emptying pipes in 6 hours = 6(6a - 5b)
Work done by 5 filling and 6 emptying pipes in 60 hours = 60(5a - 6b)

6(6a – 5b) = 60(5a – 6b)
∴ 6a – 5b = 50a – 60b
∴ 44a = 55b
∴ a = 5b/4

Let the tank gets filled completely in ‘m’ hours when one draining pipe and two filling pipes are on.
Work done by 2 filling and 1 emptying pipes in m hours = m(2a - b)

∴ m(2a – b) = 6(6a – 5b)

∴ $m (2 \times \frac{5}{4} b - b)$ = $6 (6 \times \frac{5}{4} b - 5 b)$

∴ $m (\frac{6 b}{4})$ = $6 (\frac{10 b}{4})$

Solving this, we get m = 10

Hence, 10.

24. CAT 2018 QA Slot 1 | Arithmetic - Time & Work CAT Question

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

(a)
36
(b)
32
(c)
45
(d)
40

25. CAT 2018 QA Slot 1 | Arithmetic - Time & Work CAT Question

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

(a)
18
(b)
22
(c)
16
(d)
20

Arithmetic - Time & Work - Previous Year CAT/MBA Questions

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