CAT Previous Year Questions: Time & Work Notes | Study Quantitative Aptitude (Quant) - CAT
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 [2021]
Correct Answer : 32
Explanation
Let the total work be 48 units. Let Amar do 'm' work, Akbar do 'k' work, and Anthony do 'n' units of work in a month. Amar and Akbar complete the project in 12 months. Hence, in a month they do 48/12 = 4 units of work. m + k = 4. Similarly, k+n = 3, and m+n = 2. Solving the three equations, we get m = 3/2, k = 5/2, n = 1/2 Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would take 48/1.5 = 32months.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 [2021]
Explanation
Let the total amount of work be 60 units. Then Anu, Vinu, and Manu do 4, 5, and 3 units of work per day respectively. On the 1^{st} day, Anu and Vinu work. Work done on the 1^{st} day = 9 units On the 2^{nd} day, Manu and Vinu work. Work done on the 2^{nd} day = 8 units This cycle goes on. And in 6 days, the work completed is 9 + 8 + 9 + 8 + 9 + 8 = 51 units. On the 7^{th} day, again Anu and Vinu work and complete the remaining 9 units of work. Thus, the number of days taken is 7 days.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 [2021]
Explanation
Let Entire work be W Now Anil worked for 24 days Bimal worked for 14 days and Charu worked for 14 days . Now Anil Completes W in 60 days so in 24 days he completed 0.4W Bimal completes W in 84 Days So in 14 Days Bimal completes = W/6 Therefore work done by charu = Therefore proportion of Charu = 13/30 x 21000 = 9100
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 [2021]
Explanation
Let Rahul work at a units/hr and Gautam at b units/hour Now as per the condition : 8a + 6b =7.5a + 7.5b so we get 0.5a = 1.5b or a = 3b Therefore total work = 8a + 6b = 8a + 2a = 10a Now Rahul alone takes 10a/10 = 10 hours.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 [2021]
Correct Answer : 3000
Explanation
Now Anil Paints in 12 Days Barun paints in 16 Days Now together Arun , Barun and Chandu painted in 6 Days Now let total work be W Now each worked for 6 days So Anil's work = 0.5W Barun's work = 6W / 16 = 3W/8 Therefore Charu's work =W/2 - 3W/8 = W/8 Therefore proportion of charu = 24000/8 = 3,000
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2019]
Explanation
Let Total work be 108 days At normal efficiency work is done in 12 days Let A' s day work = A & B' s day work = B ► A + B = 9 & ► A + B = 9…(1) ► A + 6B = 24…(2) Solving (1) & (2), A = 6 B = 3 At usual efficiency A will do the work in 108 / 6 = 18 days.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2019]
Explanation
Let total work be 40 units Anil's day work = 2 unit Sunil's 1 day work = 1 unit For the first 3 days work done = 6 unit Work done by Bimal = 4 unit Work done by A and S during this time = 30 unit Days = 30 / 3 = 10 days Total days = 10 + 3 = 13 days
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2018]
Explanation
Let the rate of each filling pipe be 'f ' litres/hr and the rate of each draining pipes be 'd' litres/hr As per the first condition given in the question, Capacity of tank will be = (6f - 5d ) x 6 …(i) And as per the second condition given in the question, Capacity of tank will be = (5f - 6d ) x 60 …(ii) Since the capacity of tank is same in both the cases, on equating (i) and (ii), we have ► (6f - 5d) x 6 = (5f - 6d) x 60 ► or, 6f - 5d = 50f - 60d ► or, 44f = 55d ► or, 4f = 5d Therefore, f = 1.25d , putting this value in eq. (i), Capacity of the tank = (6f - 5d ) x 6 = (7.5d - 5d) x 6 = 15d When 2 filling and 1 draining pipes work simultaneously, the effective rate of filling the tank = (2f - d ), Now putting f =1.25d in this eq. we have Effective rate = (2.5d - d ) = 1.5d Therefore time required to fill the empty tank = 15d / 1.5d = 10 hours.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2018]
Explanation
Let the efficiency of humans be 'E' and the efficiency of robots be ' R'. In the first case Total work done = (15E + 5R) x 30 …(i) In the second case, Total work done = (5E + 15R) x 60 …(ii) Since same work is finished in both the cases, so by equating (i) and (ii), we have : ► (15E + 5R) x 30 = (5E + 15R) x 60 ► (15E + 5R) = (5E + 15R) x 2 ► or, 15E + 5R = 10E + 30R ► or, 5E = 25R ► or, E = 5R Putting this value of E in (I), we have Total work = (15E + 5R) x 30 = (15E + R) x 30 = 480E Time taken by 15 humans = 480E / 15E days = 32 days.
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Question for CAT Previous Year Questions: Time & Work
Try yourself:When they work alone, B needs 25% more time to finish a job than A does. The 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?
[2018]
Explanation
Let the work completed by A in a day be 'a' units and that by B be 'b' units. As per question : A alone works till half the work is completed. Thus, 50% of work is done and rest 50% needs to be completed. Afterwards, A and B work together for 4 days and B works alone to complete the remaining 5% of the work. This means A and B in 4 days can complete 45% of the work. Now suppose that the total amount of work to be done is 100 units. ► So, 4 a + 4b = 45 …(i) Because B needs 25% more time than A to finish a job. ► So, 1.25 x b = a …(ii) Substituting value of a from (ii) in (i), we get ► 5b + 4b = 45 ► or, 9b = 45 ► or, b = 5 units/day Hence, B alone can finish the job in 100 / 5 = 20 days.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?
[2018]
Explanation
Let the tank be emptied everyday at 'T' pm. Let 'a' litres/hr' and 'b' litres/hr be the amount of water filled by pump A and pump B, respectively. As per question, on Monday, A alone completed filling the tank at 8 pm. Therefore, the pump A worked for (8 - T ) hours. So, the volume of the tank = a x (8 - T ) litres. Similarly, on Tuesday, B alone completed filling the tank at 6 pm. Therefore, the pump B worked for (6 - T ) hours. Hence, the volume of the tank = b x (6 - T ) litres. On Wednesday, A alone worked till 5 pm. and then B worked alone from 5 pm to 7 pm, to fill the tank. This means pump A worked for (5 - T ) hours and pump B worked for rest of the 2 hours. Hence, the volume of the tank = a x (5 - t) + (2 x b) litres. We can say that a x (8 - T ) = b x (6 - T ) = a x (5 - T ) + 2b …(i) or, a x (8 - T ) = a x (5 - T ) + 2b or, 3a = 2b…(ii) Again from (i) a x (8 - T ) = b x (6 - T) From (ii) we know that 3a = 2b So, a x (8 -T ) = (3a / 2) x (6 - T) or, T = 2 Thus, the tank gets emptied at 2 pm daily. A alone fills the tank at 8pm, thus, A takes 6 hours and pump B alone fills the tank at 6pm thus B takes 4 hours. Hence, working together, both can fill the tank in (6 x 4 ) / (6 + 4 ) = 2.4 hours or 2 hours and 24 minutes.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2018]
Explanation
Let the rate at which each inlet of type A brings water be 'a' litres per minute and from B 'b' litres per minute. Then, as per question 30 x (10a + 45b)
= 60 x (8a + 18b) or, 300a + 450b = 480a + 1080b or, 180a = 630b or, 6a = 9b, Thus, a : b = 3 : 2 or b = (2 / 3)a …(i)
Total capacity of tank = 30 x (10a + 45b) = 30[10a + 45 x (2 / 3)a ] = 1200a When 7 inlets of type A and 27 inlets of type B are open, the total efficiency
= 7a + 27b = 7a + 27 x (2 / 3) a = 25a
So, time taken = capacity of tank/total efficiency = 1200a / 25a = 48 minutes Hence, 48 min is the correct answer.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2018]
Explanation
Let the efficiency of Ramesh be R units per day and that of Ganesh be G units per day. As per question 16 ( R + G) = 17G + 7R + ( R - 0.3R) x 10 16R + 16G = 17G + 7R + 7R So, G = 2R, So total efficiency when both work together = R + G = R + 2R = 3R Hence, total work = 16 x 3R = 48R In second case, where Ramesh got sick after 7 days Work left after 7 days = 48R - 7 (3R) = 27R Time Ganesh would take to complete this work alone = 27R / 2R = 13.5 days.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2017]
Explanation
Let the rate of work of a person by Y units/day. Hence, the total work = 120Y . Given : On first day, only one person works, on the second day two people work and so on. Hence, the work done on day 1, day 2,… will be Y ,2Y ,3Y …respectively. Let the total number of days required to complete the work is n. Thus sum should be equal to 120Y. So, Y + 2Y + 3Y +…+ nY = 120Y or, 120Y = Y x n (n - 1) / 2 or, n^{2} + n - 240 = 0 or (n - 15)(n + 16) = 0 So, n = 15 or n = -16 But, n = 15 is the only positive value. Hence, it will take 15 days to complete the work.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2017]
Explanation
Let the time taken by the outlet pipe to empty the tank fully when only outlet pipe is open = T hours. Then, as per question [(1 / 8) - (1 / T )] = 1 /10 or, 1 / T = 1 / 8 - 1 /10 = 1 / 40, therefore the outlet pipe can empty the tank fully in 40 hours. Hence, time taken by the outlet pipe to make the tank half-full = 40 / 2 = 20 hours.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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
[2017]
Explanation
Amal, Bimal and Kamla can together complete the job in 4 days. Amal's contribution in 1 day =1 / 10 and Bimal's contribution = 1 / 8. So Kamal's contribution = 1 / 4 - (1 / 8 + 1 / 10) = 1 / 40
Ratio of their work = 1 / 10 : 1 / 8 : 1 / 40 = 4 : 5 : 1 So, amount of share for Kamal = 1000 x 1 /10 = ₹ 100
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2017]
Explanation
Let the rate of work of a person by Y units/day. Hence, the total work = 120Y . Given : On first day, only one person works, on the second day two people work and so on. Hence, the work done on day 1, day 2,… will be Y ,2Y ,3Y …respectively. Let the total number of days required to complete the work is n. Thus sum should be equal to 120Y. So, Y + 2Y + 3Y +…+ nY = 120Y or, 120Y = Y x n (n - 1) / 2 or, n^{2} + n - 240 = 0 or (n - 15)(n + 16) = 0 So, n = 15 or n = -16 But, n = 15 is the only positive value. Hence, it will take 15 days to complete the work.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2017]
Explanation
Let the capacity of the tank ► = LCM (4 ,10,12,20) = 60 So, work done by A, B, C =15, 6, 5, 3 respectively. Option 1 : Work Done in a minute ► = 15 - 6 - 5 - 3 = 1 So, after 30 minutes, the tank will be half filled.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2016]
Explanation
As per question, M inlet pipes can fill the M / 8^{th} part of the tank in 1 hour and N outlet pipes can empty N / 12^{th} part of the tank in 1 hour.
If all pipes are left open, in 1 hour, the tank will be filled = M / 8 - N /12 = 1 / 6 (as the tank will take 6 hours to fill). Then, 6 M - 4 N = 8, or, M = (8 + 4 N ) / 6.
There will be infinite number of solutions ( N = 1,4 ,7,10,13,16 ...) but none of the above ratios are correct. For example, above equation is solvable when M = 2,N = 1 or M = 4, N = 4. But the ratios 2 : 1 (i.e., M = 2,N = 1 ) or 1 : 1 ( M = 4, N = 4 ) are not correct because the solution of the above equation will not be an integer for values like M = 4 ,N = 2 or M = 6, N = 6.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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
[2016]
Explanation
Let your efficiency of doing some work be t days, then the efficiency of your roommate is 2t days. So, we have,
t = 45 days thus, 2t = 90 days
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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 cone 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?
[2015]
Explanation
The two inlet A and B and one outlet pipe C, fill or empty the tank as per rates tabulated below :
Given : Two of the pipes are kept open for 20 hours and the third pipe C for a lesser period. The tank is initially full and finally (volume = (1 / 3) x π x r^{2}h) the water level drops to 1 / 2 and so the volume will become (1 / 3) x π x (r / 2)^{2} x h / 2 = 1 / 8 {(1 / 3) x π x r^{2}h )}, i.e., 1 / 8^{th} of the original volume. This means 7 / 8^{th} volume of water must have drained out. From the table above, we can see that net rate of emptying the tank = 3 + 2 - 6 = 1 liter per hr. So, to drain the full tank out, when all the pipes are open, it will take 24 hrs. So, to drain 7 / 8^{th} tank = 7 x 24 / 8 = 21 hrs. Since, the 7 / 8^{th} water drained out in 20 hrs only, so one of the two inlet pipes must have opened for lesser time. Assuming that if all the three pipes were open for all 20 hrs, we can see that 1 extra unit was required to be drained or the water was not filled by closing one of the inlet pipes a little early. From the table, we can see that pipe B if opened for 1 / 2 hrs less, will fill the water by 1 litre less. So, B works for 19.5 hrs only.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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?
[2015]
Explanation
Let there be i and o inlet and outlet pipes respectively. ∴ i + o = 11…(i) Assume that the capacity of the tank is 35 units. So, inlet pipe fills 5 units and the outlet pipes empties 7 units of the tank in one hour. The completely filled tank empties in 7 hours. ∴ 7o - 5i = 5…(ii) So, now we solve the equations, and get i and o and i = 6.
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Question for CAT Previous Year Questions: Time & Work
Try yourself: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:
[2015]
Explanation
Let P do x units of work in one day. ∴ so, total work = 42x So, Q and R do 1.26x and (1.26 x 1.5 =)1.89x units of work in one day, respectively. ∴ Total work done by Q and R in one day = 1.26x + 1.89x = 3.15x So, Q and R can finish the work in (42x / 3.15x ≈) 13 days.
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