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Thinking Training of Olympiad Mathematics in the Fifth Grade of Primary School (Three Articles)
1. Party A, Party B and Party C plant trees in plots A and B, with 900 trees in plot A and 250 trees in plot B. It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees each day. Party A plants trees in Site A, Party C plants trees in Site B, Party B plants trees in Site A first, and then goes to Site B ... The two plots start and end at the same time. On what day should B be transferred from A to B? 2. There are three grasslands with an area of 5 15 and 24 mu respectively. The grass on the grass is as thick and grows as fast. The first meadow can feed 10 cows for 30 days, the second meadow can feed 28 cows for 45 days, and how many cows can the third meadow feed 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; 2+6/7 days, cost 1600 yuan. On the premise of ensuring the completion within one week, which team should be selected for the lowest cost?

A rectangular iron block is placed in a cylindrical container. Now turn on the tap and pour the water into the container. In 3 minutes, the water just passed the top of the cuboid. In another 18 minutes, the water has filled the container. 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.

5. Two bosses of Party A and Party B buy a piece of fashion at the same price, and Party B buys 1/5 sets more than Party A, and then Party A and Party B sell 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 10 this fashion. How many sets of this fashion A did you buy?

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 exactly one pool. At this time, the water injection rate of pipe A is increased by 25%, while the water injection rate of pipe B is unchanged. So, how many hours does it take for pipeline A to fill pool A and pipeline B to fill pool B?

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 catching up, Xiaoming still had 3/ 10 to go, so he got on his father's car and was sent to school by his father, so Xiaoming arrived at school five minutes earlier than he walked alone. How long does it take Xiaoming to walk from home to school?

8. Both A and B start from place A and pass through place B to place C. The distance between A and B is equal to the distance between B and C. The speed of B is 80% of that of A. It is known that B started earlier than A 1 1 minute, but stayed at place B for 7 minutes, while A kept driving to place C. Finally, B train was better than A train. Then car A will overtake car B a few minutes after car B leaves.

9. Party A and Party B have two cleaning vehicles to clean the road between things. It takes 15 hours for car A to clean alone, and 15 hours for car B to clean alone. Two cars leave from East and West at the same time. When they met, car A cleaned more than car B 12 kilometers. How many kilometers is there between East and West?

10. Today, 4 containers weigh 3 tons, 5 containers weigh 2.5 tons, 14 containers weigh 1 0.5 tons, and 7 containers weigh1ton. So how many cars with a load of 4.5 tons are needed to transport all the containers at once?

extreme

1. The length of circular metal wire is 30m, and three metal wires with length A 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 equal to? 2. 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?

3. 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?

4. 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 10.

5. Students in five classes of Grade 6 planted 65,438+000 trees. It is known that the number of trees planted in each class is different, and the ranking from the most to the least is 1 class, class 2, class 3, class 4 and class 5. 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.

6. 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?

7. There are two cylindrical containers A and B with the same height, and their inner diameters are 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?

8. Goods 104 tons, transported by truck with a load of 9 tons. It is known that a car needs 1 hour for each round trip. In fact, the car loads 1 ton every time, so it can be completed several hours in advance.

9. On the first day, the 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%. The two men processed 300 parts. How many parts did the master process the next day? How many parts did the apprentice process?

10. Struggle Primary School organized sixth-grade students to go camping and training in Baihua Mountain, and the trip 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?

Tisso

1. The cost of a commodity per piece in 72 yuan was originally sold at a fixed price, and 100 pieces could be sold every day, and the profit was 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? The speed ratio of the two trains A and B is 5: 4. Bus B leaves from Mile Mile for Station A.. When it is 72 kilometers away from Miley Miley, the A bus departs from Station A and goes to Miley Miley. The ratio of the distance between the two trains is 3: 4, so how many kilometers is the distance between Station A and bilibili?

There are 35 monkeys, big and small, going 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.

There are first prize and second prize in the math contest. It is known that (1) the proportion of winners in schools A and B is 6: 5. (2) The sum of the winners of A and B schools in the coming year accounts for 60% of the total winners of the two schools. (3) The proportion of winners in schools A and B is 5: 6. Ask a school that won the second prize.

5. 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?

6. Processing a batch of parts, originally planned to process 15 pieces every day, which can be completed in a few days. When 3/5 of the processing tasks are completed, the efficiency is improved by 20%. As a result, the task was completed 10 days in advance. How many parts are there in this batch?

7. Party A and Party B will have a10000m race on the 400m circular runway. They started from the same direction at the same time. At first, Party A's speed was 8m/s and Party B's speed was 6m/s. After catching up with Party B every time, Party A's speed dropped by 2m per second and Party B's speed dropped by 0.5m per second. This continued until Party A found that Party B was 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?

9. The sum of the ages of Party A, Party B, Party C and Party D is 64 years old. When Party A is 2 1 year old, Party B is1year old; When A/Kloc-0 was 8 years old, C was three times that of D. How old is D now?

10. A batch of parts was originally planned to process 30 pieces a day. When dealing with 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?