Aarav takes \(4\) hours to complete a task, whereas Bhavesh takes \(6\) hours to complete the same task. They start working together at their respective rates, but Bhavesh takes two breaks of equal duration during the work. Even after this, they complete the task in \(2\) hours \(30\) minutes. What is the duration of each break taken by Bhavesh?

Aarav takes \(4\) hours to complete a task, whereas Bhavesh takes \(6\) hours to complete the same task. They start working together at their respective rates, but Bhavesh takes two breaks of equal duration during the work. Even after this, they complete the task in \(2\) hours \(30\) minutes. What is the duration of each break taken by Bhavesh?

A team of 4 technicians, all working at the same constant rate, can complete a software deployment task in 20 hours. At the start of the project, only 2 technicians begin working. After every hour, 2 more technicians join the team. When the task is finally completed, how many technicians will be working at that moment?

A team of 4 technicians, all working at the same constant rate, can complete a software deployment task in 20 hours. At the start of the project, only 2 technicians begin working. After every hour, 2 more technicians join the team. When the task is finally completed, how many technicians will be working at that moment?

Two consultants, Arjun and Bhavna, can independently complete a market research project in \(a\) days and \(b\) days respectively. They work on the project alternately, each working for \(2\) consecutive days at a time. If Arjun starts first, the project gets completed in exactly \(10\) days. If Bhavna starts first, the project gets completed in \(10.5\) days. In how many days would they complete the project if they worked together throughout?

Two consultants, Arjun and Bhavna, can independently complete a market research project in \(a\) days and \(b\) days respectively. They work on the project alternately, each working for \(2\) consecutive days at a time. If Arjun starts first, the project gets completed in exactly \(10\) days. If Bhavna starts first, the project gets completed in \(10.5\) days. In how many days would they complete the project if they worked together throughout?

A construction contractor knows that \(24\) skilled workers can complete a project in \(16\) days, while \(32\) semi-skilled workers can complete the same project in \(24\) days. A team consisting of \(16\) skilled workers and \(16\) semi-skilled workers works on the project for \(12\) days. How many additional skilled workers must be added so that the remaining work is completed in exactly \(2\) more days?

A construction contractor knows that \(24\) skilled workers can complete a project in \(16\) days, while \(32\) semi-skilled workers can complete the same project in \(24\) days. A team consisting of \(16\) skilled workers and \(16\) semi-skilled workers works on the project for \(12\) days. How many additional skilled workers must be added so that the remaining work is completed in exactly \(2\) more days?

Two data entry operators, Anand and Balan, are assigned to complete a digital ledger. Anand can complete the entire ledger in \(20\) days working alone, while Balan can completely delete/erase a finished ledger in \(30\) days. Anand starts the work on Day 1, and they work on alternate days. Anand works to build the ledger, while Balan works to erase it at his constant rate. If they continue this alternate pattern, in how many days will the ledger get completed for the first time? (Assume that once the ledger is completely built, they stop working immediately).

Two data entry operators, Anand and Balan, are assigned to complete a digital ledger. Anand can complete the entire ledger in \(20\) days working alone, while Balan can completely delete/erase a finished ledger in \(30\) days. Anand starts the work on Day 1, and they work on alternate days. Anand works to build the ledger, while Balan works to erase it at his constant rate. If they continue this alternate pattern, in how many days will the ledger get completed for the first time? (Assume that once the ledger is completely built, they stop working immediately).

Two technicians, Arjun and Bharat, working together can complete a server installation project in 4 days 19 hours 12 minutes. If Arjun works at \(\frac{2}{3}\) of Bharat's speed, then how long will Bharat alone take to complete the same project?

Two technicians, Arjun and Bharat, working together can complete a server installation project in 4 days 19 hours 12 minutes. If Arjun works at \(\frac{2}{3}\) of Bharat's speed, then how long will Bharat alone take to complete the same project?

Three content writers, Anurag, Bhuvan, and Gautam, working together, can finish an editing project in \(6\) hours less time than Anurag alone, in \(1\) hour less time than Bhuvan alone, and in one-half the time needed by Gautam when working alone. Let \(h\) be the number of hours needed by Anurag and Bhuvan working together to finish the project. Then \(h\) equals:

Three content writers, Anurag, Bhuvan, and Gautam, working together, can finish an editing project in \(6\) hours less time than Anurag alone, in \(1\) hour less time than Bhuvan alone, and in one-half the time needed by Gautam when working alone. Let \(h\) be the number of hours needed by Anurag and Bhuvan working together to finish the project. Then \(h\) equals:

A project manager estimated that his team of \(10\) software developers could complete a data migration project in \(110\) days, assuming no server outages. (Assume that the team does not work on days with a server outage, and that outages are the only factor preventing them from working). On day \(61\), after having experienced a total of \(5\) days of server outages over the first \(60\) days, the manager onboarded \(6\) additional software developers to finish the project early. If the entire project was completed in exactly \(100\) total days, how many days of server outages occurred after day \(60\)?

A project manager estimated that his team of \(10\) software developers could complete a data migration project in \(110\) days, assuming no server outages. (Assume that the team does not work on days with a server outage, and that outages are the only factor preventing them from working). On day \(61\), after having experienced a total of \(5\) days of server outages over the first \(60\) days, the manager onboarded \(6\) additional software developers to finish the project early. If the entire project was completed in exactly \(100\) total days, how many days of server outages occurred after day \(60\)?

A large chemical storage tank is filled using two industrial inlets, \(P_1\) and \(P_2\). Working alone, \(P_1\) can fill the completely empty tank in \(8\) hours, while \(P_2\) can fill it in \(12\) hours. Both inlets are opened simultaneously to fill the empty tank. The plant supervisor plans to open a drainage valve, \(P_3\), which can empty a full tank completely in \(8\) hours, at the exact moment the tank becomes half-filled, so that the tank finishes filling precisely when he returns. However, due to a technical glitch, valve \(P_3\) opens early—exactly when the tank is only one-third filled. If the supervisor returns exactly as originally planned, what percentage of the tank is still empty?

A large chemical storage tank is filled using two industrial inlets, \(P_1\) and \(P_2\). Working alone, \(P_1\) can fill the completely empty tank in \(8\) hours, while \(P_2\) can fill it in \(12\) hours. Both inlets are opened simultaneously to fill the empty tank. The plant supervisor plans to open a drainage valve, \(P_3\), which can empty a full tank completely in \(8\) hours, at the exact moment the tank becomes half-filled, so that the tank finishes filling precisely when he returns. However, due to a technical glitch, valve \(P_3\) opens early—exactly when the tank is only one-third filled. If the supervisor returns exactly as originally planned, what percentage of the tank is still empty?

A large town reservoir is connected to three electric pumps, P1, P2, and P3, which can fill the reservoir separately in \(5\) hours, \(10\) hours, and \(15\) hours, respectively. All three pumps are opened simultaneously to fill the empty reservoir. It is observed that during the first hour, pumps P1 and P2 operate at only \(\frac{3}{4}\) of their normal efficiency. Simultaneously, pump P3 operates at only \(\frac{2}{3}\) of its normal efficiency for the first \(2\) hours. After their respective initial periods, all pumps operate at their full normal efficiency. What is the total time required to fill the reservoir completely?

A large town reservoir is connected to three electric pumps, P1, P2, and P3, which can fill the reservoir separately in \(5\) hours, \(10\) hours, and \(15\) hours, respectively. All three pumps are opened simultaneously to fill the empty reservoir. It is observed that during the first hour, pumps P1 and P2 operate at only \(\frac{3}{4}\) of their normal efficiency. Simultaneously, pump P3 operates at only \(\frac{2}{3}\) of its normal efficiency for the first \(2\) hours. After their respective initial periods, all pumps operate at their full normal efficiency. What is the total time required to fill the reservoir completely?

Three data analysts, Amit, Balram, and Chitra, can independently complete a market research project in \(15\) days, \(20\) days, and \(30\) days, respectively. They begin working together on the project, but after some days, Chitra leaves. A total payout of Rs. \(18000\) is disbursed for the entire project, with Balram receiving Rs. \(6000\) more than Chitra. For how many days did Amit work on the project?

Three data analysts, Amit, Balram, and Chitra, can independently complete a market research project in \(15\) days, \(20\) days, and \(30\) days, respectively. They begin working together on the project, but after some days, Chitra leaves. A total payout of Rs. \(18000\) is disbursed for the entire project, with Balram receiving Rs. \(6000\) more than Chitra. For how many days did Amit work on the project?

A project manager estimated that a team of employees could complete a housing project in \(100\) days. If the team had \(10\) fewer employees, it would take \(10\) days more to complete the same project. How many employees were originally in the team?

A project manager estimated that a team of employees could complete a housing project in \(100\) days. If the team had \(10\) fewer employees, it would take \(10\) days more to complete the same project. How many employees were originally in the team?

Three delivery executives worked on the same assignment over a period of 30 days. During the project, each of them remained absent for a few days. One executive was absent for 10 days more than the second executive, while the third executive completed one-third of the total work. Assuming all three executives have the same efficiency, by how many days was the first executive absent more than the third executive?

Three delivery executives worked on the same assignment over a period of 30 days. During the project, each of them remained absent for a few days. One executive was absent for 10 days more than the second executive, while the third executive completed one-third of the total work. Assuming all three executives have the same efficiency, by how many days was the first executive absent more than the third executive?

Three valves operate on a water storage tank in a fixed cycle. Valve A fills the tank in 10 hours, Valve B fills it in 20 hours, and Valve C empties the full tank in 30 hours. Each valve is opened individually for exactly one hour and then closed. The valves operate repeatedly in the order A, B, and then C. Initially, the tank is \(\frac{1}{4}\) full. After how much time will the tank begin to overflow?

Three valves operate on a water storage tank in a fixed cycle. Valve A fills the tank in 10 hours, Valve B fills it in 20 hours, and Valve C empties the full tank in 30 hours. Each valve is opened individually for exactly one hour and then closed. The valves operate repeatedly in the order A, B, and then C. Initially, the tank is \(\frac{1}{4}\) full. After how much time will the tank begin to overflow?

A construction company hired a certain number of workers to complete a project within the planned schedule. After working for 14 days, \(\frac{1}{4}\) of the workers left the project. The remaining workers then took as many days to complete the unfinished work as the original workforce would have taken to complete the entire project. In how many days was the project completed?

A construction company hired a certain number of workers to complete a project within the planned schedule. After working for 14 days, \(\frac{1}{4}\) of the workers left the project. The remaining workers then took as many days to complete the unfinished work as the original workforce would have taken to complete the entire project. In how many days was the project completed?

A manufacturing unit uses four types of conveyor channels: Channel A, Channel B, Channel C and Channel D. Each channel can either add material to a storage bin (inlet) or remove material from it (outlet), but cannot do both. There are 5 storage bins of equal capacity.

Bin P is connected to Channel A and Channel B Bin Q is connected to Channel A and Channel C Bin R is connected to Channel A and Channel D Bin S is connected to Channel B and Channel C Bin T is connected to Channel C and Channel D

The time taken by the first three bins (P, Q and R) to get completely filled are in the ratio \(1:2:4\), while the time taken by bins S and T to get completely filled are in the ratio \(7:10\). Which of the following channels must be outlet channels?

A manufacturing unit uses four types of conveyor channels: Channel A, Channel B, Channel C and Channel D. Each channel can either add material to a storage bin (inlet) or remove material from it (outlet), but cannot do both. There are 5 storage bins of equal capacity.

Bin P is connected to Channel A and Channel B Bin Q is connected to Channel A and Channel C Bin R is connected to Channel A and Channel D Bin S is connected to Channel B and Channel C Bin T is connected to Channel C and Channel D

The time taken by the first three bins (P, Q and R) to get completely filled are in the ratio \(1:2:4\), while the time taken by bins S and T to get completely filled are in the ratio \(7:10\). Which of the following channels must be outlet channels?

A warehouse supervisor is trying to pack \(30\) cartons into a storage rack. Every \(30\) seconds, the supervisor places \(3\) cartons into the rack. However, immediately after each such \(30\)-second interval, a trainee mistakenly removes \(2\) cartons from the rack.

How much time, in minutes, will it take for all \(30\) cartons to be in the rack for the first time?

A warehouse supervisor is trying to pack \(30\) cartons into a storage rack. Every \(30\) seconds, the supervisor places \(3\) cartons into the rack. However, immediately after each such \(30\)-second interval, a trainee mistakenly removes \(2\) cartons from the rack.

How much time, in minutes, will it take for all \(30\) cartons to be in the rack for the first time?

A team of \(17\) workers can construct a boundary wall of length \(20\) m in \(18\) days, working \(8\) hours per day. How many additional workers must be hired so that a similar wall of length \(39\) m can be constructed in at most \(6\) days, if each worker works \(9\) hours per day?

A team of \(17\) workers can construct a boundary wall of length \(20\) m in \(18\) days, working \(8\) hours per day. How many additional workers must be hired so that a similar wall of length \(39\) m can be constructed in at most \(6\) days, if each worker works \(9\) hours per day?

Three pipes are connected to an empty water tank of capacity \(7000\) litres. Pipe A fills the tank at the rate of \(100\) litres per minute, Pipe B fills it at the rate of \(25\) litres per minute, and Pipe C drains water at the rate of \(50\) litres per minute.

The pipes are operated in a repeating cycle as follows: Pipe A is opened for \(1\) minute and then closed. Pipe B is opened for \(1\) minute and then closed. Pipe C is opened for \(1\) minute and then closed.

This cycle continues until the tank is completely filled. How long will it take to fill the tank?

Three pipes are connected to an empty water tank of capacity \(7000\) litres. Pipe A fills the tank at the rate of \(100\) litres per minute, Pipe B fills it at the rate of \(25\) litres per minute, and Pipe C drains water at the rate of \(50\) litres per minute.

The pipes are operated in a repeating cycle as follows: Pipe A is opened for \(1\) minute and then closed. Pipe B is opened for \(1\) minute and then closed. Pipe C is opened for \(1\) minute and then closed.

This cycle continues until the tank is completely filled. How long will it take to fill the tank?

A cylindrical water tank is initially filled up to one-fifth of its total capacity. If the outlet valve at the bottom is opened, the water currently present in the tank will drain out completely in \(1\) hour. If the outlet remains closed and only the inlet pipe is opened, the tank fills from its current level to full capacity in \(2\) hours.

The inlet pipe is opened at time \(t=0\). After \(30\) minutes, the outlet valve is also opened and both remain open thereafter. In how much total time from the start will the tank become completely full?

A cylindrical water tank is initially filled up to one-fifth of its total capacity. If the outlet valve at the bottom is opened, the water currently present in the tank will drain out completely in \(1\) hour. If the outlet remains closed and only the inlet pipe is opened, the tank fills from its current level to full capacity in \(2\) hours.

The inlet pipe is opened at time \(t=0\). After \(30\) minutes, the outlet valve is also opened and both remain open thereafter. In how much total time from the start will the tank become completely full?

A manufacturing unit produces matching keychains and tags. One machine produces only keychains while another produces only tags. The keychain machine produces 400 keychains per minute and must be stopped for 15 minutes after producing 2000 keychains. The tag machine produces 300 tags per minute and must be stopped for 15 minutes after producing 3000 tags. If both machines start operating simultaneously, what is the minimum time required to produce 12000 matching pairs of keychains and tags?

A manufacturing unit produces matching keychains and tags. One machine produces only keychains while another produces only tags. The keychain machine produces 400 keychains per minute and must be stopped for 15 minutes after producing 2000 keychains. The tag machine produces 300 tags per minute and must be stopped for 15 minutes after producing 3000 tags. If both machines start operating simultaneously, what is the minimum time required to produce 12000 matching pairs of keychains and tags?

Rohan starts painting the boundary wall of a coaching centre on the first day. On the second day, \(2\) more boys join him. On the third day, \(3\) more boys join him, and this pattern continues. If the entire wall is painted in exactly \(20\) days, then in how many days can \(10\) girls paint the same wall completely, given that each girl paints twice as fast as each boy?

Rohan starts painting the boundary wall of a coaching centre on the first day. On the second day, \(2\) more boys join him. On the third day, \(3\) more boys join him, and this pattern continues. If the entire wall is painted in exactly \(20\) days, then in how many days can \(10\) girls paint the same wall completely, given that each girl paints twice as fast as each boy?

A contractor has to distribute Rs. \(351.78\) as wages among a male worker, a female worker, and a trainee. The male worker worked for \(27\) days, the female worker for \(23\) days, and the trainee for \(19\) days. In a fixed time, the female worker and the trainee together can do the same amount of work as the male worker. Also, the male worker and the trainee together can do \(1.5\) times the work done by the female worker. How much wage should the male worker receive?

A contractor has to distribute Rs. \(351.78\) as wages among a male worker, a female worker, and a trainee. The male worker worked for \(27\) days, the female worker for \(23\) days, and the trainee for \(19\) days. In a fixed time, the female worker and the trainee together can do the same amount of work as the male worker. Also, the male worker and the trainee together can do \(1.5\) times the work done by the female worker. How much wage should the male worker receive?

A cylindrical water tank in an apartment society has radius \(5\) m and height \(8\) m. At noon, the tank is \(\frac{3}{4}\) full. Every minute, \(0.08\pi \text{ m}^3\) of water is drained from the tank, while \(0.03\pi \text{ m}^3\) of water is added to it. Additionally, starting at \(1\) p.m. and then at every hour on the hour, an extra \(4\pi \text{ m}^3\) of water is drained instantly. From noon, how many hours will it take to drain the entire tank?

A cylindrical water tank in an apartment society has radius \(5\) m and height \(8\) m. At noon, the tank is \(\frac{3}{4}\) full. Every minute, \(0.08\pi \text{ m}^3\) of water is drained from the tank, while \(0.03\pi \text{ m}^3\) of water is added to it. Additionally, starting at \(1\) p.m. and then at every hour on the hour, an extra \(4\pi \text{ m}^3\) of water is drained instantly. From noon, how many hours will it take to drain the entire tank?

Three workers, Ravi, Bharat, and Chetan, working together can complete a project in \(30\) days. They start the project together. Ravi works for \(3\) days and rests on the \(4\)th day. Bharat works for \(5\) days and rests for the next \(2\) days. Chetan works for \(7\) days and rests for the next \(3\) days. If all three workers work at the same rate, in how many days will the project be completed?

Three workers, Ravi, Bharat, and Chetan, working together can complete a project in \(30\) days. They start the project together. Ravi works for \(3\) days and rests on the \(4\)th day. Bharat works for \(5\) days and rests for the next \(2\) days. Chetan works for \(7\) days and rests for the next \(3\) days. If all three workers work at the same rate, in how many days will the project be completed?