CAT Arithmetic > Time & Work PYQs

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

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

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna is the same job. The 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

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

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

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

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

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

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

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

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

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

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

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

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 $10 \mathrm{pm}$. Instead, if pipe $A$ is opened at $2 \mathrm{pm}$ and pipe $B$ is opened at $4 \mathrm{pm}$, then the tank becomes full at $6 \mathrm{pm}$. If pipe $B$ is not opened at all, then the time, in minutes, taken to fill the tank is

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 Rs. $21000$ for the job, then the share of Charu, in INR, proportionate to the work done by him, is

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

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

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?

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?

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?

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?

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 water tank has inlets of two types $A$ and $B$. All inlets of type $A$ when open, bring in water at the same rate. All inlets of type $B$, when open, bring in water at the same rate. The empty tank is completely filled in $30$ minutes if $10$ inlets of type $A$ and $45$ inlets of type $B$ are open, and in $1$ hour if $8$ inlets of type $A$ and $18$ inlets of type $B$ are open. In how many minutes will the empty tank get completely filled if $7$ inlets of type $A$ and $27$ inlets of type $B$ are open?

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump $A$ or pump $B$ or both start working until the tank is full. On Monday, $A$ alone completed filling the tank at $8 \mathrm{pm}$. On Tuesday, B alone completed filling the tank at $6 \mathrm{pm}$. On Wednesday, $A$ alone worked till $5 \mathrm{pm}$, and then B worked alone from $5 \mathrm{pm}$ to $7 \mathrm{pm}$, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

Ramesh and Ganesh can together complete a work in $16$ days. After seven days of working together, Ramesh got sick and his efficiency fell by $30 \%$. As a result, they completed the work in $17$ days instead of $16$ days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?

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 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?

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 tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in $8$ hours. If the outlet pipe is open then the inlet pipe fills the empty tank in $10$ hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

Amal can complete a job in $10$ days and Bimal can complete it in $8$ days. Amal, Bimal and Kamal together complete the job in $4$ days and are paid a total amount of Rs $1000$ as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

A person can complete a job in $120$ days. He works alone on Day $1$. On Day $2$, he is joined by another person who also can complete the job in exactly $120$ days. On Day $3$, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?