Previous Year OMET Questions for Arithmetic

1. XAT 2020 QADI | Arithmetic - Time & Work

X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes a day off after every 3 days of work, Y takes a day off after every 4 days of work and Z takes a day off after every 5 days of work.

Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days

If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?

A.
2 days
B.
3.5 days
C.
2.5 days
D.
4 days
E.
5 days

2. IIFT 2019 QA | Arithmetic - Time & Work

A group of women in a society decided to execute interior and exterior decoration of the society in a week’s time. Since 11 women dropped out every day from the second day, the entire decoration was completed on 12th day. How many women participated at the beginning? (Answer to the nearest integer)

A.
137
B.
141
C.
145
D.
148

3. IIFT 2019 QA | Arithmetic - Time & Work

Rohit purchased a cistern which had a leakage. The cistern can be filled by two inlet pipes, which can individually fill the cistern in 12 min and 15 min respectively. Despite leakage, the two inlet pipes together can fill the cistern in 20 min. How long will it take to empty the completely full the cistern due to leakage?

A.
10 mins
B.
12 mins
C.
15 mins
D.
16 mins

4. XAT 2018 QADI | Arithmetic - Time & Work

Abdul, Bimal, Charlie and Dilbar can finish a task in 10, 12, 15 and 18 days respectively. They can either choose to work or remain absent on a particular day. If 50 percent of the total work gets completed after 3 days, then, which of the following options is possible?

A.
Each of them worked for exactly 2 days.
B.
Bimal and Dilbar worked for 1 day each, Charlie worked for 2 days and Abdul worked for all 3 days.
C.
Abdul and Charlie worked for 2 days each, Dilbar worked for 1 day and Bimal worked for all 3 days.
D.
Abdul and Dilbar worked for 2 days each, Charlie worked for 1 day and Bimal worked for all 3 days.
E.
Abdul and Charlie worked for 1 day each, Bimal worked for 2 days and Dilbar worked for all 3 days.

5. IIFT 2018 QA | Arithmetic - Time & Work

Ram, Ravi and Ratan can alone finish an assignment in 9 days, 12 days and 15 days respectively. They decide to complete a work by working in turns. Ram works alone on Monday, Ravi does the work alone on Tuesday, followed by Ratan working alone on Wednesday & so on. What proportion of the complete work is done by Ravi?

A.
2/9
B.
12/47
C.
1/3
D.
4/9

6. IIFT 2018 QA | Arithmetic - Time & Work

Nitin installed an overhead tank on the roof of his newly constructed house. Three taps are connected to the tank: 2 taps A and B to fill the tank and one tap C to empty it. Tap A alone can fill the tank in 12 hours, while tap B alone takes one and a half times more time than tap A to fill the tank completely. Tap C alone can empty a completely filled tank in 36 hours. Yesterday, to fill the tank, Nitin first opened tap A, and then after 2 hours opened tap B also. However after 6 hours he realised that tap C was open from the very beginning. He quickly closes tap C. What will be the total time required to fill the tank?

A.
8 hours 48 minutes
B.
8 hours 30 minutes
C.
9 hours 12 minutes
D.
9 hours 36 minutes

7. XAT 2017 QADI | Arithmetic - Time & Work

Four two-way pipes A, B, C and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions the tank would be half filled after 30 minutes?

A.
Pipe A filled and pipes B, C and D drained
B.
Pipe A drained and pipes B, C and D filled
C.
Pipes A and D drained and pipes B and C filled
D.
Pipes A and D filled and pipes B and C drained
E.
None of the above

8. IIFT 2017 QA | Arithmetic - Time & Work

Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and 75 days. They started the work together but Nikhil left 5 days after the start and Somesh left 2 days before the completion of the work. In how many days will the work be completed?

A.
$25 \frac{1}{7}$
B.
$50 \frac{1}{7}$
C.
$35 \frac{5}{7}$
D.
$40 \frac{5}{7}$

9. IIFT 2017 QA | Arithmetic - Time & Work

An overhead tank, which supplies water to a settlement, is filled by three bore wells. The first two bore wells operating together fill the tank in the same time as taken by the third bore well to fill it. The second bore well fills the tank 10 hours faster than the first one and 8 hours slower than the third one. The time required by the third bore well to fill the tank alone is:

A.
9 hours
B.
12 hours
C.
18 hours
D.
20 hours

10. XAT 2016 QADI | Arithmetic - Time & Work

A water tank has M inlet pipes and N outlet pipes. An inlet pipe can fill the tank in 8 hours while an outlet pipe can empty the full tank in 12 hours. If all pipes are left open simultaneously, it takes 6 hours to fill the empty tank. What is the relationship between M and N?

A.
M : N = 1 : 1
B.
M : N = 2 : 1
C.
M : N = 2 : 3
D.
M : N = 3 : 2
E.
None of the above

11. IIFT 2016 QA | Arithmetic - Time & Work

In the marketing management course of an MBA programme, you and your roommate can complete an assignment in 30 days. If you are twice as efficient as your roommate, the time required by each to complete the assignment individually is

A.
45 days and 90 days
B.
30 days and 60 days
C.
40 days and 120 days
D.
45 days and 135 days

12. IIFT 2015 QA | Arithmetic - Time & Work

A tank is connected with both inlet pipes and outlet pipes. Individually, an inlet pipe can fill the tank in 7 hours and an outlet pipe can empty it in 5 hours. If all the pipes are kept open, it takes exactly 7 hours for a completely filled-in tank to empty. If the total number of pipes connected to the tank is 11, how many of these are inlet pipes?

A.
2
B.
4
C.
5
D.
6

13. IIFT 2015 QA | Arithmetic - Time & Work

Three carpenters P, Q and R are entrusted with office furniture work. P can do a job in 42 days. If Q is 26% more efficient than P and R is 50% more efficient than Q, then Q and R together can finish the job in approximately:

A.
11 days
B.
13 days
C.
15 days
D.
17 days

14. XAT 2015 QA | Arithmetic - Time & Work

Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?

A.
Pipe A was open for 19 hours.
B.
Pipe A was open for 19 hours 30 minutes.
C.
Pipe B was open for 19 hours 30 minutes.
D.
Pipe C was open for 19 hours 50 minutes.
E.
The situation is not possible.

Answer: Option C

Explanation :

Let the capacity of the tank be 24x litres.

Pipes A and B fill 3x and 2x litres per hour while pipe C empties 6x litres in an hour.

Let radius of the cone be r and height be h.

$\frac{1}{3} π r^{2} h = 24 x$

∴ πr²h = 72x

For first 19 hours, water inside the cone = 24x + 57x + 38x – 114x = 5x litres

∆ABE ∼ ∆ACD

If AC = 2AB, CD = 2BE

∴ BE = r/2 and AB = h/2

After 50% reduction in the height of the water, volume

$= \frac{1}{3} π {(r / 2)}^{2} (h / 2) = \frac{π r^{2} h}{24} = \frac{72 x}{24} = 3 x$

Option 1: Pipe A was open for 19 hours.

i.e., B and C were open for 1 more hour.

∴ 2x – 6x = –4x

The cone will have 5x – 4x = x litres of water.

∴ Option 1 is eliminated.

Option 2: Pipe A was open for 19 hours 30 minutes.

i.e., B and C were open for 1 more hour and A for 30 more minutes.

∴ 2x – 6x + 1.5x = –2.5x

The cone will have 5x – 2.5x = 2.5x litres of water

∴ Option 2 is eliminated.

Option 3: Pipe B was open for 19 hours 30 minutes.

i.e., A and C were open for 1 more hour and B for 30 more minutes.

∴ 3x – 6x + 1x = –2x

The cone will have 5x – 2x = 3x litres of water.

∴ Option 3 would be the possible option.

Hence, option 3.

15. IIFT 2013 QA | Arithmetic - Time & Work

A mother along with her two sons is entrusted with the task of cooking Biryani for a family get-together. It takes 30 minutes for all three of them cooking together to complete 50 percent of the task. The cooking can also be completed if the two sons start cooking together and the elder son leaves after 1 hour and the younger son cooks for further 3 hours. If the mother needs 1 hour less than the elder son to complete the cooking, how much cooking does the mother complete in an hour?

A.
33.33%
B.
50%
C.
66.67%
D.
None of the above

Answer: Option B

Explanation :

Let the number of days required to complete the work by mother, elder son and younger son be m, e and y hours respectively.

Therefore, work done by mother; elder son and younger son in one day is 1/m, 1/e and 1/n respectively.

Also m = e – 1 (∵ Mother take one hour less than the elder son)

Based on the conditions given,

$\frac{1}{m}$ + $\frac{1}{e}$ + $\frac{1}{y}$ = 1 ...(1)

$\frac{1}{e}$ + $\frac{1}{y}$ + $\frac{3}{y}$ = 1 ...(2)

$\frac{1}{y}$ = $\frac{e - 1}{4 e}$

Also m = e – 1

Substituting values of (1/m) and (1/y) in (1)

$\frac{1}{e - 1}$ + $\frac{1}{e}$ + $\frac{e - 1}{4 e}$ = 1

Solving,

e = 3

Therefore, m = 2 and work done in 1 hour = 50%

Hence, option 2.

16. IIFT 2013 QA | Arithmetic - Time & Work

Capacity of tap Y is 60% more than that of X. If both the taps are opened simultaneously, they take 40 hours to fill the rank. The time taken by Y alone to fill the tank is

A.
60 hours
B.
65 hours
C.
70 hours
D.
75 hours

Answer: Option B

Explanation :

Tap X does a units of work in 1 hour.

∴ Tap Y does 1.6a units of work in 1 hour.

∴ In 1 hour Tap X and Y together do 2.6a units of work.

∴ Work done by Tap X and Y in 40 hours = 2.6a × 40

∴ Time taken by Tap Y alone to do this work

= $\frac{2.6 a \times 40}{1.6 a}$ = 65 hours

Hence, option 2.

17. IIFT 2012 QA | Arithmetic - Time & Work

12 men can complete a work in ten days. 20 women can complete the same work in twelve days. 8 men and 4 women started working and after nine days 10 more women joined them. How many days will they now take to complete the remaining work?

A.
2 days
B.
5 days
C.
8 days
D.
10 days

Answer: Option A

Explanation :

Let one man complete the piece of work in m days and let one woman complete the piece of work in n days.

∴ $\frac{12}{m}$ = $\frac{1}{10}$ and $\frac{20}{w}$ = $\frac{1}{12}$

∴ $\frac{1}{m}$ = $\frac{1}{120}$ and $\frac{1}{w}$ = $\frac{1}{240}$

Let n be the number of days after 9 days that the work takes to get over.

∴ 9 $(\frac{8}{m} + \frac{4}{w})$ + n $(\frac{8}{m} + \frac{4}{w} + \frac{10}{w})$ = 1

∴ 9 $(\frac{1}{15} + \frac{1}{60})$ + n $(\frac{1}{15} + \frac{1}{60} + \frac{1}{24})$ = 1

∴ $\frac{3}{4}$ + $\frac{15 n}{120}$ = 1

∴ n = 2

Hence, option 1.

18. IIFT 2011 QA | Arithmetic - Time & Work

In Bilaspur village, 12 men and 18 boys completed construction of a primary health center in 60 days, by working for 7.5 hours a day. Subsequently the residents of the neighbouring Harigarh village also decided to construct a primary health center in their locality, which would be twice the size of the facility build in Bilaspur. If a man is able to perform the work equal to the same done by 2 boys, then how many boys will be required to help 21 men to complete the work in Harigarh in 50 days, working 9 hours a day?

A.
45 boys
B.
48 boys
C.
40 boys
D.
42 boys

19. IIFT 2011 QA | Arithmetic - Time & Work

A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5th of the work is finished. How many additional men may be employed so that work may be completed on time, each man now working 9 hours per day?

A.
56 men
B.
65 men
C.
46 men
D.
None of the above

Answer: Option A

Explanation :

Work done by 104 men, working 8 hours a day, in 30 days = 104 × 8 × 30 man hours.

This is 2/5th of the total work.

= 104 × 8 × 30 × $\frac{5}{2}$ × $\frac{3}{5}$ = 104 × 4 × 90 man hours.

∴ Remaining work, which is 3/5th of the total work

Let a more men be employed to complete this work.

∴ (104 + a) × 9 × (56 – 30) = 104 × 4 × 90

∴ a = 56

Hence, option 1.

20. IIFT 2010 QA | Arithmetic - Time & Work

Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work.

A.
7.2 days
B.
9.5 days
C.
11.5 days
D.
None of these

Answer: Option A

Explanation :

Let Dr. Gupta take x days to complete the evaluation work.

∴ Dr. Sharma takes x + 10 days

As Dr. Gupta is 40% more efficient than Dr. Sharma, we have

$\frac{1}{x}$ = $\frac{1.4}{x + 10}$

∴ x = 25

∴ x + 10 = 35

Also, Dr. Sharma is 20% more efficient than Dr. Singh.

∴ If Dr. Singh takes y days to complete the evaluation work,

$\frac{1}{35}$ = $\frac{1.2}{y}$

∴ y = 42

Now, let Dr. Singh complete the evaluation work in n days after Dr. Gupta has worked for 10 days and Dr. Sharma has worked for 15 days.

∴ $\frac{10}{25}$ + $\frac{15}{35}$ + $\frac{n}{42}$ = 1

∴ n = 7.2

Hence, option 1.

21. IIFT 2010 QA | Arithmetic - Time & Work

Three pipes A, B and C are connected to a tank. These pipes can fill the tank separately in 5 hours, 10 hours and 15 hours respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at 3/4th of their normal rates for the first hour after which they supplied water at the normal rate. Pipe C supplied water at 2/3rd of its normal rate for first 2 hours, after which it supplied at its normal rate. In how much time, tank would be filled.

A.
1.05 Hours
B.
2.05 Hours
C.
3.05 Hours
D.
None of these

Answer: Option C

Explanation :

Let the pipes work for n hours.

By the given conditions,

$\frac{1}{5 \times \frac{4}{3}}$ + $\frac{1}{10 \times \frac{4}{3}}$ + (n - 1) $[\frac{1}{5} + \frac{1}{10}]$ + $\frac{2}{15 \times \frac{3}{2}}$ + $\frac{n - 2}{15}$ = 1

∴ $\frac{3}{20}$ + $\frac{3}{40}$ + (n - 1) $\frac{3}{10}$ + $\frac{4}{45}$ + $\frac{n - 2}{15}$ = 1

∴ $\frac{9}{40}$ + $\frac{3 n - 3}{10}$ + $\frac{4}{45}$ + $\frac{n - 2}{15}$ = 1

∴ $\frac{9 n - 9}{30}$ + $\frac{2 n - 4}{30}$ = 1 - $\frac{9}{40}$ - $\frac{4}{45}$

∴ $\frac{11 n - 13}{30}$ = $\frac{360 - 81 - 32}{360}$

∴ 11n - 13 = $\frac{247 \times 30}{360}$

∴ n ≈ 3.05

Hence, option 3.

22. IIFT 2009 QA | Arithmetic - Time & Work

Because of economic slowdown, a multinational company curtailed some of the allowances of its employees. Rashid, the marketing manager of the company whose monthly salary has been reduced to Rs.42000 is unable to cut down his expenditure. He finds that there is a deficit of Rs.2000 between his earnings and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. Rashid has a saving of Rs.60000 which will be used to fill this deficit. After his savings get exhausted, Rashid would start borrowing from his friends. How soon will he start borrowing?

A.
10th month
B.
11th month
C.
12th month
D.
13th month

Answer: Option D

Explanation :

If Rashid’s savings fill his deficit for n months,

60000 = $\frac{n}{2}$ [4000 + (n - 1)500]

∴ n² + 7n - 240 = 0

∴ n ≈ 12.38

∴ Rashid savings last for 12 months, after which he has to start borrowing from the 13^th month.

Hence, option 4.

23. IIFT 2009 QA | Arithmetic - Time & Work

Aditya, Vedus and Yuvraj alone can do a job in 6 weeks, 9 weeks and 12 weeks respectively. They work together for 2 weeks. Then Aditya leaves the job. Vedus leaves the job a week earlier to the completion of the work. The job would be completed in:

A.
4 weeks
B.
5 weeks
C.
7 weeks
D.
None of the above

Answer: Option A

Explanation :

Aditya, Vedus and Yuvraj do (1/6), (1/9) and (1/12) of the work respectively in a week. Let the total time taken to complete the work be n weeks.

Then,

2 $(\frac{1}{6})$ + (n - 1) $(\frac{1}{9})$ + n $(\frac{1}{12})$ = 1

∴ $\frac{12 + 4 (n - 1) + 3 n}{36}$ = 1

∴ n = 4

Hence, option 1.

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

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