Time & Work — Set #2 | Practice

{"setId":"c20749ad-0bb4-44f8-9626-5ae81d21c926","setTitle":"Time and Work 2 – UPSC CSAT","topicName":"Time & Work","topicSlug":"time-work","setNumber":2,"totalQuestions":10,"questions":[{"id":"df3de526-d5c4-4cad-9173-afcbd8676564","order":1,"statement":"A tank can be completely filled by two pipes 'A' and 'B' alone in 45 minutes and 36 minutes, respectively. A third pipe 'C' can empty the tank in 30 minutes. If 'A' and 'B' are initially opened for 9 minutes, and then pipe 'C' is also opened. In how much more time (in minutes), the tank will be completely filled?","options":{"A":"27","B":"24","C":"33","D":"36"},"correctOption":"C","solution":"Using 180 litres (LCM of 45,36,30): Pipe A fills 4 litres/min, Pipe B fills 5 litres/min, Pipe C empties 6 litres/min. In 9 minutes with A and B open, tank filled = 9×9=81 litres. With all three open, combined rate = 4+5-6=3 litres/min. Remaining volume = 180-81=99 litres. Time required = 99/3 = 33 minutes."},{"id":"b70d1f23-3c22-484e-a352-b21bcfcee6fb","order":2,"statement":"The three taps can fill a container in 30 minutes, 40 minutes and 60 minutes, respectively. What percentage of the container would be filled if all the three taps are opened for 4 minutes.","options":{"A":"20%","B":"25%","C":"30%","D":"40%"},"correctOption":"C","solution":"Using 120 litres (LCM of 30,40,60): Tap efficiencies are 4, 3, and 2 litres/minute respectively, totaling 9 litres/minute. In 4 minutes, volume filled = 9×4=36 litres. Percentage filled = (36/120)×100 = 30%."},{"id":"64c3c96f-d023-4526-a39c-e5857283783f","order":3,"statement":"An application is developed by a pro developer and Intern in 41/3 days. They worked on alternate days, with Pro developer began the work first. The Intern can finish the application; working alone in 60 days. The Pro developer alone can finish 8 times the same task in how many days?","options":{"A":"66 days","B":"63 days","C":"72 days","D":"75 days"},"correctOption":"B","solution":"Total days=41/3. Since Pro started first and they alternate, Pro works 7 days and Intern works 41/3-7=20/3 days. Intern's work in 20/3 days = (1/60)×(20/3)=1/9 of the work. Remaining 8/9 of work done by Pro in 7 days, so Pro completes whole work in 7×(9/8)=63/8 days. Pro completes 8 times the work in (63/8)×8=63 days."},{"id":"2560c6a1-b4cf-4a57-91c6-589e6283fa27","order":4,"statement":"'P' can do a certain work in the same time in which 'Q' and 'R' together can do it. If 'P' and 'Q' together could do it in 6 days and 'R' alone in 30 days, then 'Q' alone could do it in:","options":{"A":"8 days","B":"12 days","C":"14 days","D":"15 days"},"correctOption":"D","solution":"Using 30 units (LCM of 6,30): (P+Q)'s efficiency=5 units/day, R's efficiency=1 unit/day. Since P's efficiency equals (Q+R)'s efficiency: efficiency of (P+Q)=efficiency of (Q+R+Q)=5, so 2×Q+1=5, giving Q's efficiency=2 units/day. Time for Q alone = 30/2=15 days."},{"id":"b21142b3-a4d7-4667-adc6-d7e046b41ec0","order":5,"statement":"A pipe can fill a cistern in 12 hours and another pipe can empty it in 10 hours. If they are opened together, in how many hours will cistern be empty?","options":{"A":"60 hours","B":"30 hours","C":"22 hours","D":"24 hours"},"correctOption":"A","solution":"In one hour, filling pipe does 1/12 of tank, emptying pipe does 1/10. Net emptying rate per hour = 1/10-1/12 = (12-10)/120 = 1/60. Time to empty the tank = 60 hours."},{"id":"1a9a2b62-ba1b-46d0-980e-c98a7115d639","order":6,"statement":"A Bridge can be built by 35 people in 80 days. So they started constructing it. Due to new offers 10 people left after working for Z days. If the construction of the Bridge was completed in 96 days, then what is the value of Z?","options":{"A":"50","B":"60","C":"30","D":"40"},"correctOption":"D","solution":"Total work=35×80=2800 person-days. For Z days, 35 people work, then for remaining (96-Z) days, 25 people work. Equation: 35×Z+25×(96-Z)=2800. Solving: 35Z+2400-25Z=2800, giving 10Z=400, so Z=40."},{"id":"f66ce747-4a76-4c2b-b2f2-99c9789ab082","order":7,"statement":"Virat alone can do a window fitting of a house for 4750 Rs in 9.5 days. But with the help of Raj the work is completed in 6 days. What is the share of Raj that Virat should pay him?","options":{"A":"1500 Rs","B":"1750 Rs","C":"1550 Rs","D":"1600 Rs"},"correctOption":"B","solution":"Using LCM of 9.5 and 6 = 114 units total work: Virat's efficiency = 114/9.5=12 units/day. Combined efficiency (Virat+Raj) = 114/6=19 units/day. Raj's efficiency = 19-12=7 units/day. Payment per unit = 4750/19=250 Rs. Raj's share = 7×250=1750 Rs."},{"id":"f070a3c9-cff0-46ba-bf32-5dd1b78ac97a","order":8,"statement":"Three wiremen namely Raja, Bala and Sada of a Electricity board are supposed to attach bulbs on municipality poles. Working independently they can do a whole task in 24 days, 27 days and 36 days, respectively. Raja alone works on Wednesday, Bala alone works on Thursday, Sada works on Friday, Raja again works on Saturday and so on. Consider the following statements. Statement (I): The work will be finished on Wednesday. Statement (II): The work will be finished in 29 days. Which of the above statement/statements is/are false?","options":{"A":"Only Statement (I)","B":"Only Statement (II)","C":"Both Statement (I) and Statement (II)","D":"Neither Statement (I) nor Statement (II)"},"correctOption":"C","solution":"Using 216 units (LCM of 24,27,36): Raja does 9 units/day, Bala does 8 units/day, Sada does 6 units/day. Each 3-day cycle (Raja, Bala, Sada) completes 9+8+6=23 units. After 9 such cycles (27 days), 207 units are done. Remaining 9 units are completed by Raja on the next day (day 28), which falls on Tuesday, not Wednesday. So the work finishes on Tuesday in 28 days, making both statements false."},{"id":"db9ff637-fb93-41a9-856c-581c64bd4cd8","order":9,"statement":"Swami, Rupa & Krishna can paint a house in 15, 20 and 30 days respectively. On the first day Swami is Assisted by Rupa, and on the second day Krishna assists Swami. This 2 day cycle is repeated starting with Swami and Rupa, till the work gets completed. How long (in days) could it take to complete the work?","options":{"A":"9 1/6","B":"10 1/6","C":"8 1/6","D":"11 1/6"},"correctOption":"A","solution":"Using 60 units (LCM of 15,20,30): Swami=4 units/day, Rupa=3 units/day, Krishna=2 units/day. Day 1 (Swami+Rupa): 7 units. Day 2 (Swami+Krishna): 6 units. Each 2-day cycle completes 13 units. After 4 cycles (8 days), 52 units done. On day 9, Swami+Rupa work again, adding 7 units, totaling 59 units (only 1 unit short of 60). The remaining 1 unit takes 1/6 of a day. Total time = 9 1/6 days."},{"id":"a3535bbe-ac6a-457e-92e8-1be2863b79f9","order":10,"statement":"Andy, Brian and Carl can finish a task in 32 days, 48 days and 96 days respectively. Andy started the work, Brian joined him after 4 days. If Carl joined them after 7 days from the beginning, How many days Andy worked till the finishing of task?","options":{"A":"14.5 days","B":"20.5 days","C":"18.5 days","D":"16.5 days"},"correctOption":"C","solution":"Using 96 units (LCM of 32,48,96): Andy=3, Brian=2, Carl=1 unit/day. Andy works alone for 4 days = 12 units. Then Andy+Brian work together for 3 more days (until day 7) = 5×3=15 units. Total by day 7 = 12+15=27 units. Remaining = 96-27=69 units, completed by all three together at 6 units/day, taking 69/6=11.5 days. Total days Andy worked = 7+11.5 = 18.5 days."}]}