Time & Work (Negative Work) Time & Work (Negative Work) Time & Work (Negative Work) 1 / 20 1) Aman can build a wall in 15 days, and Bharat can build it in 10 days, but Chintu can destroy it in 30 days. If they all work together, how long will it take to complete the wall? 6 days 8 days 10 days 12 days Aman’s rate = 1/15Bharat’s rate = 1/10Chintu’s destruction rate = -1/30Net work = 1/15 + 1/10 - 1/30LCM of 15, 10, 30 is 30Work per day: (2 + 3 - 1)/30 = 4/30 = 1/6Total time = 6 days 2 / 20 2) Pipe A fills a tank in 12 hours, and Pipe B fills it in 18 hours, while a leakage can empty it in 36 hours. If all are opened together, how long will it take to fill the tank? 8 hours 9 hours 10 hours 12 hours Filling rates: 1/12 + 1/18Leakage rate: -1/36LCM of 12, 18, 36 is 36Net rate = (3 + 2 - 1) / 36 = 4/36 = 1/9Total time = 9 hours 3 / 20 3) A group of workers can dig a pit in 25 days, while another group can do the same in 30 days. But a refilling machine refills it in 75 days. How long will it take to dig the pit? 10 days 12 days 15 days 18 days Digging rates: 1/25 + 1/30Refilling rate: -1/75LCM of 25, 30, 75 is 150Net rate = (6 + 5 - 2) / 150 = 9/150 = 1/15Total time = 15 days 4 / 20 4) A pipe can fill a tank in 20 minutes, while another fills it in 30 minutes. A third pipe empties it in 40 minutes. If all pipes are opened together, how long will it take to fill the tank? 10 minutes 12 minutes 15 minutes 18 minutes Filling rates: 1/20 + 1/30Emptying rate: -1/40LCM of 20, 30, 40 is 120Net rate = (6 + 4 - 3) / 120 = 7/120Total time = 120/10 = 12 minutes 5 / 20 5) A road construction team can complete a road in 50 days, and another team can complete it in 75 days, but a natural erosion process removes 1/150 of the road daily. If all happen together, how long will it take to finish the road? 30 days 32 days 35 days 40 days Work rates: 1/50 + 1/75 - 1/150LCM of 50, 75, 150 is 150Net rate = (3 + 2 - 1) / 150 = 4/150 = 1/30Total time = 30 days 6 / 20 6) A bricklayer lays a wall in 15 days, another in 20 days, and a storm damages it in 60 days. If all act together, how long will the wall take? 10 days 12 days 14 days 16 days LCM of 15, 20, 60 is 60Work rate = (4 + 3 - 1) / 60 = 6/60 = 1/12Total time = 12 days 7 / 20 7) A pipe fills a tank in 9 hours, another in 12 hours, while a leak empties it in 36 hours. How long will it take to fill the tank? 5 hours 6 hours 7 hours 8 hours Net work = (4 + 3 - 1) / 36 = 6/36 = 1/6Total time = 6 hours 8 / 20 8) One painter paints a house in 20 days, another in 30 days, while rain washes paint off at 1/60 rate per day. How long will painting take? 12 days 14 days 15days 16 days Net work = (3 + 2 - 1) / 60 = 4/60 = 1/15Total time = 15 days 9 / 20 9) A machine produces 500 items/day, another produces 400/day, but 100 items are defective each day. How many days to produce 3000 items? 3 days 4 days 5 days 6 days Net production = (500 + 400 - 100) = 800/dayTotal time = 3000/800 = 4 days 10 / 20 10) A writer completes a book in 40 days, another in 50 days, while an editor removes 2 pages/day. How long to complete a 200-page book? 20 days 22 days 24 days 25 days Work rate = (5 + 4 - 2) / 200 = 7/200Total time = 200/8 = 25 days 11 / 20 11) A team can repair a road in 12 days, while another team takes 18 days. But daily traffic damage adds 1/36 of the road's damage per day. How long will it take to repair the road? 6 days 8 days 9 days 10 days LCM of 12, 18, 36 is 36Work rate = (3 + 2 - 1) / 36 = 4/36 = 1/9Total time = 9 days 12 / 20 12) A reservoir is filled by a pipe in 20 hours and another in 25 hours. Evaporation removes 1/50 of the water every hour. How long to fill the reservoir? 10 hours 12 hours 15 hours 18 hours LCM of 20, 25, 50 is 100Net work = (5 + 4 - 2) / 100 = 7/100Total time = 12 hours 13 / 20 13) A builder constructs a house in 60 days, another in 80 days, while storms damage 1/120 of the house daily. How long will it take to build? 30 days 32 days 36 days 40 days Net work = (2 + 1.5 - 0.833) / 120 = 2.667/120 = 1/40Total time = 40 days 14 / 20 14) A team repairs a bridge in 45 days, another in 60 days, while river currents damage 1/90 per day. How long will it take to repair? 18 days 20 days 24 days 30 days Net work = (2 + 1.5 - 1) / 90 = 2.5/90 = 1/30Total time = 30 days 15 / 20 15) A group cleans a pond in 30 days, another in 40 days, but algae grow back at a rate of 1/120 per day. How long to clean the pond? 20 days 24 days 28 days 32 days Net work = (4 + 3 - 1) / 120 = 6/120 = 1/24Total time = 24 days 16 / 20 16) A gardener removes weeds in 16 days, another in 24 days, but weeds regrow at a rate of 1/48 per day. How long to clear weeds? 10 days 12 days 14 days 16 days Net work = (3 + 2 - 1) / 48 = 4/48 = 1/12Total time = 12 days 17 / 20 17) One person mows a lawn in 5 hours, another in 7 hours, but grass regrows at 1/14 per hour. How long to mow? 2 hours 3 hours 4 hours 5 hours Net work = (1/5 + 1/7 - 1/14) = (14 + 10 - 5) / 70 = 19/70Total time = 70/19 ≈ 4 hours 18 / 20 18) A printer prints in 8 hours, another in 12 hours, but paper jams delay printing by 1/24 per hour. How long to print all pages? 4 hours 5 hours 6 hours 7 hours Net work = (3 + 2 - 1) / 24 = 4/24 = 1/6Total time = 6 hours 19 / 20 19) A person picks fruit in 10 hours, another in 15 hours, while birds eat 1/30 of the fruit per hour. How long to pick all fruit? 5 hours 6 hours 7 hours 8 hours Net work = (3 + 2 - 1) / 30 = 4/30 = 1/6Total time = 6 hours 20 / 20 20) One worker cleans a park in 20 days, another in 25 days, but visitors litter at 1/50 per day. How long to clean the park? 10 days 12 days 15 days 18 days Net work = (5 + 4 - 2) / 100 = 7/100Total time = 12 days Your score isThe average score is 0% 0% Restart quiz