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Mathematical engineering question bank
1. Party A, Party B and Party C plant trees in two plots A and B respectively, with 900 trees in plot A and 0/250 trees in plot B. It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees every day, of which Party A plants trees in plot B, and Party B plants trees in plot A first and then moves to plot B..

2. There are three grasslands with an area of 5 15 and 24 mu respectively. The grass on the grassland is as thick and grows as fast. The first grassland can feed 10 cows for 30 days, and the second grassland can feed 28 cows for 45 days. How many cows can eat on the third grass for 80 days?

3. A project, contracted by both parties, can be completed in 2.4 days and needs to be paid 1800 yuan; Contracted by Team B and Team C, it can be completed in 3+3/4 days, and it needs to be paid 1500 yuan; Contracted by two teams, Party A, Party B and Party C, it can be completed in 2+6/7 days at a cost of 1.600 yuan. On the premise of ensuring the completion within one week, which team will spend the least?

There is a rectangular iron block in the cylindrical container. Now turn on the tap and pour the water into the container. In 3 minutes, the water surface is just above the top of the cuboid. /kloc-After 0/8 minutes, the container has been filled with water. It is known that the height of a container is 50 cm and the height of a cuboid is 20 cm. Find the ratio of the bottom area of a cuboid to the bottom area of a container.

Two bosses, A and B, bought a fashion at the same price, and B bought 1/5 sets more than A, and then they sold them at profit margins of 80% and 50% respectively. After both of them were sold out, A still made more profits than B, just enough for him to buy 65,438+00 sets of this fashion, which A bought at the beginning.

6. There are two water pipes A and B, and water is injected into two pools with the same size at the same time. At the same time, the water injection ratio of A and B is 7: 5. After 2+ 1/3 hours, the sum of the water injected into A and B is just a pool. At this time, the water injection rate of pipe A is increased by 25%, while pipe B remains unchanged.

Xiao Ming walks from home to school in the morning. When he ran halfway, his father found that Xiao Ming's math book was left at home, and then he rode to deliver it to Xiao Ming. When he caught up, Xiao Ming still had 3/ 10 to go. Xiao Ming got on his father's car at once and was sent to school by his father, so Xiao Ming arrived at school five minutes earlier than walking alone. How long does it take Xiaoming to walk from home to school?

8. Car A and car B both start from place A and pass through place B to place C. The distance between the two places is equal to the distance from place B to place C. The speed of car B is 80% of that of car A. It is known that car B started earlier than car A 1 1 minute, but stayed in place B for 7 minutes, but car A drove all the way to place C. Finally, car B was later than car A..

9. Two cleaning vehicles, A and B, perform road cleaning tasks between things. It takes 10 hour for car A to be cleaned alone, and 15 hour for car B to be cleaned alone. Two cars leave from east and west at the same time. When they met, car A was cleaner than car B12km. How many kilometers is it between East and West?

/kloc-4 containers of 0/0.3 tons, 5 containers of 2.5 tons, 1 0.5 tons/4 containers, and 7 containers of1ton. So how many cars with a load of 4.5 tons are needed to transport all the containers at once?

1 1. Both the master and the apprentice * * * processed 170 parts, and the number of parts processed by the master was 1/3 more than that processed by the apprentice, so how many parts did the apprentice process?

12. Both a cart and a car drive from A to B, and the speed of the cart is 80% of that of the car. It is known that the big car started 17 minutes earlier than the small car, but it stopped at the midpoint of the two places for 5 minutes before continuing to B. However, after the small car started, it went straight to the second place without stopping. Finally, the bus came second before the bus. It is also known that the bus departs from the first place at 10 in the morning. So when did the bus catch up with the bus in the morning?

13. For a manuscript, it takes 14 hours for Party A to type alone, and 20 hours for Party B to type alone. If Party A types 1 hour first, then Party B types 1 hour instead of Party A, and then Party A types 1 hour instead of Party B. .................................................................

1There are 3 yellow balloons in 4.2 yuan and 2 flower balloons in 3 yuan. The school * * * bought 32 balloons, 4 of which were fewer than yellow balloons. What balloons do schools spend more money on?

15. The sailing speed is 60m/min. In a river with a velocity of 20m/min, it takes 3 hours and 30 minutes for a ship to travel from an upstream port to a downstream location and back again. How long does it take for the ship to get from the upstream port to the downstream?

16. Granary A contains 43 tons of flour and Granary B contains 37 tons of flour. If the flour from granary B is loaded into granary A, the remaining flour after granary B is full accounts for 1/2 of granary B's capacity. If the flour from granary A is put into granary B, after granary B is full, the remaining flour from granary A accounts for 1/3 of granary A's capacity. How many tons of flour can each granary hold?

17. When A is divided by B and B is divided by C, the quotient is equal and the remainder is 2. The sum of A and B is 478. So what is the sum of a, b and c?

18. A car traveling from A to B will arrive 1 hour later than the original time if it slows down 10%. If you drive at the original speed 1 80km, you will arrive1hour earlier than the original time. What's the distance between a and b?

19. A school participated in the military training queue performance competition and organized a phalanx team. If there are 60 students in each class, there must be at least 4 classes in this phalanx. If there are 70 students in each class, there must be at least 3 classes in this phalanx. How many people should this phalanx consist of?

20.a, B and C lathes process square and round parts. It is known that two out of every three parts machined by lathe are round; Three out of every four parts machined by lathe B are round; Four fifths of the parts processed by lathe C are round. On this day, three lathes * * * processed 58 round parts, and the number ratio of square parts processed was 4: 3: 3. So how many parts were processed by the three lathes on this day?

2 1. The length of circular metal wire is 30m, and three metal wires with length a are intercepted and five metal wires with length b are intercepted. If two metal wires with length b are intercepted, the remaining metal wires are 0.4m shorter, and if two metal wires with length a are intercepted, they are 2m shorter. How many meters is the length a?

22. A company wants to transport two kinds of building materials, A and B, to the construction site. Building materials A weigh 700kg each, including 120 * * *, and building materials B weigh 900kg each, including 80 * * *. It is known that a car can transport up to 4 tons at a time, so how many times do five identical cars have to be transported at the same time?

23. The distance from Wang Lijia to the school is longer than the distance to the gymnasium 1/4. One day, Wang Li watched the game in the gym and walked home in 17 minutes. After a short rest, it took him 25 minutes to walk to school, which was slower than coming back from the gym 15 meters. How far is it from Wang Lijia to school?

24. Master and apprentice cooperate to complete a project. Because of their good cooperation, the master's work efficiency has been improved110, and the apprentice's work efficiency has been improved 1/5. After six days of cooperation, two-fifths of the whole project was completed, and then the apprentice worked alone for six days. At this time, the project still has 65438+.

25. Students in five classes of Grade Six planted 65,438+000 trees. As we all know, the number of trees planted in each class is different, and the ranking from the most to the least is just 1, 2, 3, 4 and 5 classes. It is also known that the number of trees planted in 1 is the sum of the number of trees planted in Class 2 and Class 3, and the number of trees planted in Class 2 is the sum of the number of trees planted in Class 4 and Class 5.

26. A runs 13 km per hour, B runs 1 1 km per hour, and B runs 20 minutes longer than A. As a result, B runs 2 km longer than A. How many kilometers did B run?

27. There are two cylindrical containers, A and B, with inner diameters of 6 cm and 8 cm respectively. Container A is full of water and container B is empty. All the water in container A was poured into container B, and the water depth in container B was measured to be 2 cm lower than 7/8 of the container height. What is the height of the container?

28. The cargo 104 tons is transported by 9-ton truck. It is known that a car needs 1 hour for each round trip. In fact, every time the car is loaded 1 ton, it can be completed a few hours in advance.

29. On the first day, master and apprentice processed 225 parts, and on the second day, new technology was adopted. The number of parts processed by the master increased by 24% compared with the first day, and the number of apprentices increased by 45%. Two people processed 300 parts. How many parts did the master process the next day? How many parts did the apprentice process?

30. Struggle Primary School organizes sixth-grade students to go camping and training in Baihua Mountain, and the journey is increased by 2 kilometers every day. I went for four days and came back for three days. How many kilometers is the school from Baihua Mountain?

3 1. The standard for charging electricity in a certain place is: the monthly electricity consumption does not exceed 50 degrees, and the electricity fee is charged at 50 cents per degree; If it exceeds 50 degrees, the excess will be charged at 80 points per degree. Every month, user A pays 3 yuan and 30 cents more than user B. How many kWh did users A and B use this month?

Master Wang plans to process a batch of parts in two hours. When there were 160 parts left, the machine broke down and the efficiency was lower than before 1/5. As a result, the task was completed 20 minutes later than originally planned. How many parts are there in this batch?

33. Mom gave Honghong some money to buy New Year cards, including three kinds of cards: A, B and C. Each card of A is 1.20 yuan. How much did Mom give Hong Hong to buy one card instead of eight cards B and six cards B? How much is the second card?

34. An old man has five sons and three houses. Before he died, he made a will and gave three houses to his three sons. As compensation, the three sons who were assigned to the house each took out 1.200 yuan and divided it equally among the two sons who were not assigned to the house. Everyone says this distribution is fair and reasonable, so how much is each house worth?

35. Xiaoming and Xiaoyan have less than 20 picture books. If Xiaoming gives Xiaoyan an A, Xiaoming's picture book is twice as big as Xiaoyan's. If Xiaoyan gives it to Xiao Amin, Xiao Ming's picture book is three times as big as Xiaoyan's. How many picture books do Xiaoming and Xiaoyan have?

36. There are three kinds of balls *** 160. If 1/3 of the red ball, 1/4 of the yellow ball and 1/5 of the white ball are removed, 120 remains. If 1/5 of the red ball, 1/4 of the yellow ball and 1/3 of the white ball are removed, 1 16 remains. How many yellow balls are there? (2) How many red balls and white balls are there?

37. My father, brother and sister are all 64 years old now. When my father was three times as old as my brother, my sister was nine years old. When my brother is twice as old as my sister, my father is 34 years old. How old are they now?

38.B is between A and C, and A delivers letters from B to A.. 10 minutes later, B delivers another letter from B. 10 minutes later, C found that A and B had just reversed the two letters, so he rode from B to catch up with A and B in order to transfer the letters. It is known that a and b have the same speed.

39. There are 94 workers in Workshop A and Workshop B, processing 1998 bamboo chairs every day. Due to different equipment and technology, each worker in Workshop A can only produce 15 bamboo chairs per day, while each worker in Workshop B can produce 43 bamboo chairs per day. How many more bamboo chairs does Workshop A produce every day than Workshop B?

40. It takes 10 minutes for Party A to go home from school, and 14 minutes for Party B. It is known that the distance for Party B to go home is 1/6 longer than that for Party A, and Party A walks 12 meters longer than that for Party B every minute. So how many meters is the distance for Party B to go home?

4 1. The cost of a commodity per piece in 72 yuan was originally sold at a fixed price, and 100 pieces can be sold every day, and the profit of each piece accounts for 25% of the cost. Later, it was sold at 90% of the fixed price, and the daily sales volume increased to 2.5 times. According to this calculation, how many yuan does the daily profit increase?

42. The speed ratio of the two trains A and B is 5: 4. The second train leaves from Mile Mile for Station A.. When it is 72 kilometers away from Miley Miley, the first train goes from Station A to Miley Miley Miley. The ratio of the distance between the two trains is 3: 4, so what is the distance between Station A and bilibili?

43. There are 35 monkeys, big and small, who go to pick peaches together. In the absence of the Monkey King, a big monkey can pick 15kg and a small monkey can pick 1 1kg in an hour. When the Monkey King is present to supervise, each monkey, regardless of size, can pick 12kg per hour.

44. There are first prize and second prize in the math contest. It is known (1) that the ratio of winners in two schools is 6: 5. (2) The sum of the winners of the two schools in the coming year will account for 60% of the total winners of the two schools. (3) The ratio of winners of the two schools is 5: 6. Ask a school to win the second prize.

45. It is known that the walking speed ratio of Xiaoming and Xiao Qiang is 2: 3, and that of Xiao Qiang and Xiaogang is 4: 5. It is known that Xiao Gang walks 420 meters more than Xiao Ming in 10 minute, so how many meters does Xiao Ming walk less than Xiao Qiang in 20 minutes?

46. It was originally planned to process 15 pieces a day, which could be completed in a few days. When 3/5 of the processing tasks are completed, the efficiency is improved by 20%. Therefore, the task was completed 65,438+00 days ahead of schedule. How many parts are there in this batch?

47.a and B competed in the10000m race on the 400m circular track. They started from the same starting point at the same time. At first, the speed of A was 8m/s, and the speed of B was 6m/s. Every time I caught up with B, the speed of A dropped by 2m per second, and the speed of B dropped by 0.5m per second. This continued until A found B catching up from behind for the first time.

Xiao Ming goes to school from home. If he walks 1.5km more every hour than before, he only needs 4/5 of the original time. If he walks 1.5km less per hour than before, how long will it take him to walk this section?

49. A, B, C and D are all 64 years old now. When a is 2 1 year, b is1year; When A/Kloc-0 was 8 years old, C was three times that of D. How old is D now?

50. A batch of parts was originally planned to process 30 pieces a day. When processing 1/3, due to the improvement of technology, the work efficiency increased by 10%, and the task was completed four days ahead of schedule. How many parts are there in this batch?