Time & Work — Set #1 | Practice

{"setId":"8e889826-e9c6-4051-976e-101541f77f67","setTitle":"Time and Work – UPSC CSAT","topicName":"Time & Work","topicSlug":"time-work","setNumber":1,"totalQuestions":10,"questions":[{"id":"5dc13f6e-2539-473d-9553-0a3ec39680fe","order":1,"statement":"'M' does 2/3rd part of the work in 6 days and 'N' does 3/4th of the same work in 6 days. If both work together, then find the required time to complete the same work.","options":{"A":"5 1/17 days","B":"4 3/17 days","C":"4 4/17 days","D":"5 2/3 days"},"correctOption":"C","solution":"Time for M to complete whole work = 6×(3/2) = 9 days. Time for N to complete whole work = 6×(4/3) = 8 days. Using 72 units (LCM of 8,9): M's one day work = 72/9 = 8 units, N's one day work = 72/8 = 9 units. Combined, they complete 72/(8+9) = 72/17 = 4 4/17 days."},{"id":"d9e66299-6169-489f-9c65-90ce189c09f7","order":2,"statement":"'P' can do a piece of work in 15 days. 'Q' can do this work in 20 days. 'P' started the work alone, after how many days should 'Q' join him, so that the work is finished in 12 days?","options":{"A":"4 days","B":"7 days","C":"8 days","D":"9 days"},"correctOption":"C","solution":"Using 60 units (LCM of 15,20): P's one day work = 4 units, Q's one day work = 3 units. If P works alone for 12 days, work done = 12×4 = 48 units. Remaining work = 60-48 = 12 units, which Q must complete in 12/3 = 4 days. So Q should join 12-4 = 8 days after P started."},{"id":"6ccfb4f5-c4ed-4985-bf9f-d87c27d117cb","order":3,"statement":"8 men or 12 boys can do a work in 16 days. The number of days that 12 men and 6 boys would finish the same work is:","options":{"A":"8 days","B":"14 days","C":"10 days","D":"9 days"},"correctOption":"A","solution":"Let efficiency of a man=M, boy=B. Total work = 8M×16 = 128M = 12B×16 = 192B, so M/B=192/128=3/2, meaning M=1.5B. Efficiency of 12 men+6 boys = 12(1.5B)+6B = 18B+6B = 24B. Time required = Total work/Efficiency = 192B/24B = 8 days."},{"id":"91a95e55-9089-4f7c-bade-be268c1a8b97","order":4,"statement":"Manoj and Vijay alone can do a work in 15 days and 20 days, respectively. If they work alternatively starting from Manoj, then the work will be completed in:","options":{"A":"8 days","B":"10 days","C":"14 days","D":"17 days"},"correctOption":"D","solution":"Using 60 units (LCM of 15,20): Manoj's one day work = 4 units, Vijay's = 3 units. Working alternately, in 2 days they complete 4+3=7 units. In 16 days (8 cycles), they complete 56 units, taking 16 days. Remaining work = 4 units, done by Manoj (next in sequence) at 4 units/day, taking 1 more day. Total = 17 days."},{"id":"ecb03b47-a0bb-4a1a-9bef-a4a4c86c67ff","order":5,"statement":"If 5 men can complete a piece of work in 6 days by working 7 hours a day, then in how many days can 7 men do the same work by working 6 hours a day?","options":{"A":"5 days","B":"4 days","C":"4 1/2 days","D":"4 1/3 days"},"correctOption":"A","solution":"Using M1D1H1=M2D2H2 (work being constant): 5×6×7 = 7×D×6, so D = (5×6×7)/(7×6) = 5 days."},{"id":"691b012f-aaa4-4359-b2df-500f4334d6e1","order":6,"statement":"Raju do a work in 10 days, while Ravi do it in 15 days. If they work alternatively and first Raju started the work, in how many days will the work be finished?","options":{"A":"15 days","B":"12 days","C":"13 days","D":"9 days"},"correctOption":"B","solution":"Using 30 units (LCM of 10,15): Raju's efficiency = 3 units/day, Ravi's = 2 units/day. Working alternately, in 2 days they complete 3+2=5 units. To complete 30 units, time required = 30×(2/5) = 12 days."},{"id":"984b6060-1cab-4a90-bd4e-bb5de7ef2670","order":7,"statement":"'P' and 'Q' tgether can do a piece of work in 24 days, 'Q' and 'R' together can do the same work in 30 days, while 'R' and 'P' together can do it in 40 days. In how many days, 'Q' alone can complete the same work?","options":{"A":"40 days","B":"30 days","C":"35 days","D":"36 days"},"correctOption":"A","solution":"Using 120 units (LCM of 24,30,40): (P+Q)=5 units/day, (Q+R)=4 units/day, (R+P)=3 units/day. Sum of all pairs = 2×(P+Q+R) = 5+4+3=12, so P+Q+R=6 units/day. Since R+P=3, Q's efficiency = 6-3=3 units/day. Time for Q alone = 120/3 = 40 days."},{"id":"4ae0ce4d-ecb6-4bab-a0a5-206f48a64990","order":8,"statement":"'P' and 'Q' completes a job in 18 days when they work together while 'P', 'Q' and 'R' together can finish the same job in 12 days. In how many days 'R' alone will finish the job?","options":{"A":"24 days","B":"28 days","C":"30 days","D":"36 days"},"correctOption":"D","solution":"Using 36 units (LCM of 12,18): (P+Q+R)'s efficiency = 36/12 = 3 units/day. (P+Q)'s efficiency = 36/18 = 2 units/day. R's efficiency = 3-2 = 1 unit/day. Time for R alone = 36/1 = 36 days."},{"id":"c5c755cd-d448-4d97-8456-3208ecbbc7fa","order":9,"statement":"Rahul works twice fast as Manoj. If both of them together complete a work in 24 days. Rahul alone can complete it in how many days?","options":{"A":"30 days","B":"36 days","C":"40 days","D":"48 days"},"correctOption":"B","solution":"Since Rahul is twice as fast as Manoj, if Rahul takes x days, Manoj takes 2x days. Combined work rate: 1/x+1/2x = 1/24, giving (2+1)/2x = 1/24, so 3/2x=1/24, meaning x=36. Rahul alone completes the work in 36 days."},{"id":"de6422af-1f66-4c77-800a-b941d2fbcc4e","order":10,"statement":"'P' and 'Q' together can do 3/5th part of a work in 6 days. If 'Q' alone can do the whole work in 15 days, then find the time taken by 'P' alone to finish the work.","options":{"A":"20 days","B":"24 days","C":"28 days","D":"30 days"},"correctOption":"D","solution":"Time for (P+Q) to complete full work = 6×(5/3) = 10 days. Using 30 units (LCM of 10,15): (P+Q)'s one day work = 3 units, Q's one day work = 2 units. So P's one day work = 3-2 = 1 unit. Time for P alone = 30/1 = 30 days."}]}