Time & Work ( Alternate Work ) Time & Work (Alternative Work) Time & Work (Alternative Work) 1 / 20 20) Arjun and Bhavya can complete a task in 18 and 24 days, respectively. They work on alternate days, but every 4th day is a rest day. How many days will they take to finish the work? 22 days 24 days 26 days 28 days Arjun’s 1-day work = 1/18Bhavya’s 1-day work = 1/24Work in 3 days (before rest day) = (1/18 + 1/24) = (4 + 3)/72 = 7/72Work in 12 days = (12/3) × 7/72 = 28/72In 24 days, 56/72 work is done.On the 25th day, Arjun works and completes the remaining 1/18.Total days = 26 days. 2 / 20 19) A machine A completes a job in 5 hours, while machine B takes 7 hours. They work alternately every hour, starting with A. How many hours will they take to complete the work? 5 hours 5.5 hours 6 hours 6.5 hours A’s 1-hour work = 1/5B’s 1-hour work = 1/7Work in 2 hours = (1/5 + 1/7) = (7 + 5)/35 = 12/35Work in 4 hours = 24/35A works in 5th hour, completing 1/5.Remaining work = 1 - (24/35 + 7/35) = 4/35B works for (4/35) ÷ (1/7) = 0.5 hours.Total time = 5.5 hours. 3 / 20 18) Amit can complete a task in 16 days, while Sumit can do it in 24 days. They work on alternate days, starting with Amit. In how many days will the work be completed? 16 days 17 days 18 days 19 days Amit’s 1-day work = 1/16Sumit’s 1-day work = 1/24Work in 2 days = (1/16 + 1/24) = (3 + 2)/48 = 5/48Work in 16 days = (16/2) × (5/48) = 40/48Remaining work = 1 - 40/48 = 8/48 = 1/6Amit works on 17th day, completing 1/16 work.Remaining work = 1/6 - 1/16 = 8/48 - 3/48 = 5/48Sumit works on 18th day, finishing it.Total days = 18 days. 4 / 20 17) Neha, Raj, and Ankit can complete a task in 20, 25, and 30 days, respectively. They work on alternate days in the order Neha → Raj → Ankit. How long will it take to complete the work? 21 days 22.5 days 24 days 26 days Neha’s 1-day work = 1/20Raj’s 1-day work = 1/25Ankit’s 1-day work = 1/30Work in 3 days = (1/20 + 1/25 + 1/30) = (15 + 12 + 10) / 600 = 37/600Work in 18 days = (18/3) × (37/600) = 222/600Remaining work = 1 - 222/600 = 378/600 = 63/100Neha works on 19th day, completing 1/20.Remaining work = 63/100 - 5/100 = 58/100Raj works on 20th day, completing 1/25 = 4/100.Remaining work = 58/100 - 4/100 = 54/100.Ankit works on 21st day, completing 1/30 = 3.33/100.Remaining work = 54/100 - 3.33/100 = 50.67/100.Neha works half a day more to complete the work.Total time = 22.5 days. 5 / 20 16) Aarav can complete a job in 12 days, and Vedant can do it in 18 days. They work on alternate 2-day cycles, starting with Aarav. How long will it take to complete the job? 14 days 15 days 16 days 17 days Aarav’s 2-day work = 2 × (1/12) = 2/12 = 1/6Vedant’s 2-day work = 2 × (1/18) = 2/18 = 1/9Work in 4 days = (1/6 + 1/9) = (3 + 2)/18 = 5/18Work in 12 days = (12/4) × (5/18) = 10/18Remaining work = 1 - 10/18 = 8/18Aarav works one more day, completing 1/12.Remaining work = 8/18 - 1/12 = 2/18.Vedant works for one more day, finishing it.Total days = 15 days. 6 / 20 15) Ajay can complete a task in 10 days, while Kunal can do it in 15 days. They work alternately every 3 days, starting with Ajay. In how many days will the work be completed? 11.5 days 12 days 12.5 days 13 days Ajay’s 1-day work = 1/10Kunal’s 1-day work = 1/15Ajay’s 3-day work = 3 × (1/10) = 3/10Kunal’s 3-day work = 3 × (1/15) = 3/15 = 1/5Work in 6 days = (3/10 + 1/5) = (3/10 + 2/10) = 5/10 = 1/2Work in 12 days = 2 × (1/2) = 1 (work completed).Since they complete exactly in 12 days, total time = 12 days. 7 / 20 14) Swati can complete a task in 25 days, and Priya can do it in 30 days. They work alternately every 2 days, starting with Swati. How long will it take to complete the work? 25 days 26 days 27 days 28 days Swati’s 1-day work = 1/25Priya’s 1-day work = 1/30Swati’s 2-day work = 2 × (1/25) = 2/25Priya’s 2-day work = 2 × (1/30) = 2/30 = 1/15Work in 4 days = (2/25 + 1/15) = (6/75 + 5/75) = 11/75Work in 24 days = 6 × (11/75) = 66/75Remaining work = 1 - 66/75 = 9/75 = 3/25Swati works one more day, completing 1/25.Remaining work = 3/25 - 1/25 = 2/25.Priya works one more day, finishing it.Total days = 27 days. 8 / 20 13) Machine A takes 8 hours, and machine B takes 12 hours to complete a task. If A starts and they alternate every hour, how long will it take to complete the work? 8.5 hours 9 hours 9.5 hours 10 hours A’s 1-hour work = 1/8B’s 1-hour work = 1/12Work in 2 hours = (1/8 + 1/12) = (3/24 + 2/24) = 5/24Work in 8 hours = 4 × (5/24) = 20/24Remaining work = 1 - 20/24 = 4/24 = 1/6A works for one more hour, completing 1/8.Remaining work = 1/6 - 1/8 = 1/24.B works for half an hour, finishing it.Total time = 9.5 hours. 9 / 20 12) Amit can complete a work in 12 days, and Raj in 16 days. They work alternately every 2 days, starting with Amit. How long will it take to complete the work? 13.5 days 14 days 14.5 days 15 days Amit’s 1-day work = 1/12Raj’s 1-day work = 1/16Amit’s 2-day work = 2 × (1/12) = 2/12 = 1/6Raj’s 2-day work = 2 × (1/16) = 2/16 = 1/8Work in 4 days = (1/6 + 1/8) = (4/24 + 3/24) = 7/24Work in 12 days = 3 × (7/24) = 21/24Remaining work = 1 - 21/24 = 3/24 = 1/8Amit works one more day, completing 1/12.Remaining work = 1/8 - 1/12 = 1/24.Raj works one more day, finishing it.Total time = 14 days. 10 / 20 11) Shreya and Kavya can complete a work in 10 and 14 days, respectively. They work alternately every 3 days, starting with Shreya. How long will it take to complete the work? 11.5 days 12 days 12.5 days 13 days Shreya’s 1-day work = 1/10Kavya’s 1-day work = 1/14Shreya’s 3-day work = 3 × (1/10) = 3/10Kavya’s 3-day work = 3 × (1/14) = 3/14Work in 6 days = (3/10 + 3/14) = (21/70 + 15/70) = 36/70 = 18/35Work in 12 days = 2 × (18/35) = 36/351 full work is done in 12 days, and extra 1/35 remains.Shreya works for half a day, finishing it.Total time = 12.5 days. 11 / 20 10) Two workers take 15 and 20 days to complete a task. They work alternately every 1 day, starting with the faster worker. Find the total time taken. 16 days 17 days 17.5 days 18 days Worker A’s 1-day work = 1/15Worker B’s 1-day work = 1/20Work in 2 days = (1/15 + 1/20) = (4/60 + 3/60) = 7/60Work in 16 days = 8 × (7/60) = 56/60Remaining work = 1 - 56/60 = 4/60 = 1/15Worker A works one more day, finishing it.Total time = 17.5 days. 12 / 20 9) Sohan can complete a task in 18 days, while Rahul takes 24 days. They work alternately every 3 days, starting with Sohan. How long will it take to complete the work? 19.5 days 20 days 20.5 days 21 days ohan’s 1-day work = 1/18Rahul’s 1-day work = 1/24Sohan’s 3-day work = 3 × (1/18) = 3/18 = 1/6Rahul’s 3-day work = 3 × (1/24) = 3/24 = 1/8Work in 6 days = (1/6 + 1/8) = (4/24 + 3/24) = 7/24Work in 18 days = 3 × (7/24) = 21/24Remaining work = 1 - 21/24 = 3/24 = 1/8Sohan works one more day, completing 1/18.Remaining work = 1/8 - 1/18 = 1/36.Rahul works half a day, finishing it.Total time = 20.5 days. 13 / 20 8) Pooja can complete a work in 28 days, while Rohan takes 35 days. They work alternately every 2 days, starting with Pooja. How long will it take to complete the work? 30 days 31 days 31.5 days 32 days Pooja’s 1-day work = 1/28Rohan’s 1-day work = 1/35Pooja’s 2-day work = 2 × (1/28) = 2/28 = 1/14Rohan’s 2-day work = 2 × (1/35) = 2/35Work in 4 days = (1/14 + 2/35) = (5/70 + 4/70) = 9/70Work in 28 days = 7 × (9/70) = 63/70Remaining work = 1 - 63/70 = 7/70 = 1/10Pooja works one more day, completing 1/28.Remaining work = 1/10 - 1/28 = 9/280.Rohan works one more day, finishing it.Total time = 31.5 days. 14 / 20 7) A machine takes 6 hours, and another machine takes 9 hours to complete a task. If they alternate every 1 hour, starting with the faster machine, how long will it take to complete the work? 6.5 hour 7 hour 7.5 hour 8 hour Machine A’s 1-hour work = 1/6Machine B’s 1-hour work = 1/9Work in 2 hours = (1/6 + 1/9) = (3/18 + 2/18) = 5/18Work in 6 hours = 3 × (5/18) = 15/18Remaining work = 1 - 15/18 = 3/18 = 1/6Machine A works one more hour, finishing it.Total time = 7 hours. 15 / 20 6) Aditi and Nitin can complete a work in 20 days and 30 days, respectively. They work alternately every 5 days, starting with Aditi. How long will the work take? 22 days 22.5 days 23 days 24 days Aditi’s 1-day work = 1/20Nitin’s 1-day work = 1/30Aditi’s 5-day work = 5 × (1/20) = 5/20 = 1/4Nitin’s 5-day work = 5 × (1/30) = 5/30 = 1/6Work in 10 days = (1/4 + 1/6) = (3/12 + 2/12) = 5/12Work in 20 days = 2 × (5/12) = 10/12Remaining work = 1 - 10/12 = 2/12 = 1/6Aditi works 2.5 more days, finishing it.Total time = 22.5 days. 16 / 20 5) Ajay can complete a work in 25 days, while Rakesh takes 40 days. They work alternately every 2 days, starting with Ajay. How long will the work take? 27 days 27.5 days 28 days 28.5 days Ajay’s 1-day work = 1/25Rakesh’s 1-day work = 1/40Ajay’s 2-day work = 2 × (1/25) = 2/25Rakesh’s 2-day work = 2 × (1/40) = 2/40 = 1/20Work in 4 days = (2/25 + 1/20) = (8/100 + 5/100) = 13/100Work in 24 days = 6 × (13/100) = 78/100Remaining work = 1 - 78/100 = 22/100 = 11/50Ajay works for 2 more days, completing 2/25 = 4/50.Remaining work = 11/50 - 4/50 = 7/50.Rakesh works for 2 more days, completing 1/20 = 5/100 = 5/50.Remaining work = 7/50 - 5/50 = 2/50 = 1/25.Ajay works for half a day, finishing it.Total time = 27.5 days. 17 / 20 4) A and B can complete a work in 10 and 15 hours, respectively. They work alternately every 1 hour, starting with A. How long will the work take? 11.5 hours 12 hours 12.5 hours 13 hours A’s 1-hour work = 1/10B’s 1-hour work = 1/15Work in 2 hours = (1/10 + 1/15) = (3/30 + 2/30) = 5/30 = 1/6Work in 12 hours = 6 × (1/6) = 1 (complete work)Total time = 12 hours. 18 / 20 3) Rekha and Tina can complete a work in 24 days and 36 days, respectively. They work alternately every 4 days, starting with Rekha. How long will it take? 28 days 28.5 days 29 days 29.5 days Rekha’s 1-day work = 1/24Tina’s 1-day work = 1/36Rekha’s 4-day work = 4 × (1/24) = 4/24 = 1/6Tina’s 4-day work = 4 × (1/36) = 4/36 = 1/9Work in 8 days = (1/6 + 1/9) = (3/18 + 2/18) = 5/18Work in 24 days = 3 × (5/18) = 15/18Remaining work = 1 - 15/18 = 3/18 = 1/6Rekha works 3 more days, completing 1/8.Remaining work = 1/6 - 1/8 = 1/24.Tina works for half a day, finishing it.Total time = 28.5 days. 19 / 20 2) Jatin can complete a work in 21 days, and Kiran takes 28 days. They work alternately every 3 days, starting with Jatin. Find the time taken to complete the work. 24.5 days 25 days 25.5 days 26 days Jatin’s 1-day work = 1/21Kiran’s 1-day work = 1/28Jatin’s 3-day work = 3 × (1/21) = 3/21 = 1/7Kiran’s 3-day work = 3 × (1/28) = 3/28Work in 6 days = (1/7 + 3/28) = (4/28 + 3/28) = 7/28 = 1/4Work in 24 days = 4 × (1/4) = 1 (complete work)Total time = 25.5 days. 20 / 20 1) Sanya and Priya can finish a work in 18 and 27 days, respectively. They work alternately every 2 days, starting with Sanya. Find the total time taken. 20.5 days 21 days 21.5 days 22 days Sanya’s 1-day work = 1/18Priya’s 1-day work = 1/27Sanya’s 2-day work = 2 × (1/18) = 2/18 = 1/9Priya’s 2-day work = 2 × (1/27) = 2/27Work in 4 days = (1/9 + 2/27) = (3/27 + 2/27) = 5/27Work in 20 days = 5 × (5/27) = 25/27Remaining work = 1 - 25/27 = 2/27.Sanya works for 1.5 more days, finishing it.Total time = 21.5 days. Your score isThe average score is 0% 0% Restart quiz
