Give some Mathematical Olympiad questions

Between Ningbo and Hangzhou, the train stops at 7 stations, and the fares at each station are different. So how many different fares are there between Ningbo and Hangzhou?

For a simplest fraction, add a number to its numerator, and the fraction is equal to 1/2. If the same number is subtracted from its numerator

, the fraction is equal to 1/6. What is the original simplest fraction?

Arrange a set of data in order from small to large (or large to small), the number in the middle (when the number of data is an odd number), or the number of the two middle data The mean (when the number of data is an even number) is called the median of this set of data. The existing set of data has 00 numbers, of which 5 numbers are between the median and the mean. If the median and the mean of this set of data are not among the 100 numbers, then this set of data The percentage of the data that is smaller than the average among the 100 data is -----

Boss Wang, who is in the clothing business, operates two stores A and B. Each store can operate at the same time. A total of 30 pieces of clothing of two styles A and B were sold, and for every piece of clothing of style A and style B sold, the gross profit of store A was 30 yuan and 40 yuan respectively, and the gross profit of store B was 27 and 36 yuan respectively. . One day, Boss Wang purchased 35 pieces of style A clothing and 25 pieces of style B clothing. How to allocate 30 pieces of clothing to each store so that Boss Wang can increase the total gross profit while ensuring that the gross profit of a store is not less than 950 yuan? What is the maximum gross profit?

A junior high school mathematics league was held in a certain area, with four middle schools A, B, C and D participating. Among the contestants, there were ***16 from A and B and 20 from B and C. There are 34 students from schools C and D, and the number of contestants from each small school is selected in the order of middle schools A, B, C, and D. Try to find the number of contestants from each middle school.

There are two points O and A on the number axis. Point O is the origin. Let the number corresponding to point A be x, and it is known that 0

Select any 9 points in a rectangle with side lengths of 2 and 4 respectively (any 3 points are not equal to the line), prove that there are at least 3 points, and the area of ??the triangle with them as vertices is not greater than 1.

1. Three people, A, B, and C, plant trees in two plots of land A and B. They want to plant 900 trees in land A and 1250 trees in land B. It is known that A, B, and C can plant trees every day. 24, 30, 32 trees. A is planting trees in land A, and C is planting trees in land B. B first plants trees in land A, and then moves to land B to plant trees. The two lands start and end at the same time. How many days after the start does B start? Transfer from A to B?

2. There are three grasslands, with an area of ??5, 15, and 24 acres respectively. The grass on the grasslands is equally thick and grows equally fast. The first grassland can be eaten by 10 cows for 30 days, and the grass on the grassland can be eaten by 10 cows for 30 days. Two pieces of grassland can feed 28 cows for 45 days. How many cows can feed the third piece of land for 80 days?

3. A certain project is contracted by teams A and B, and can be completed in 2.4 days, and a payment of 1,800 yuan is required; a project contracted by teams B and C, can be completed in 3 3/4 days, and a payment of 1,500 yuan is required. ; Contracted by two teams, A and C, it can be completed in 2 6/7 days and requires a payment of 1,600 yuan. On the premise of ensuring completion within one week, which team will be chosen to contract alone with the least cost?

4. There is a rectangular iron block in a cylindrical container. Now open the faucet and fill the container with water. In 3 minutes, the water surface just covers the top surface of the rectangular parallelepiped. After another 18 minutes, the water has filled the container. .It is known that the height of the container is 50 cm and the height of the cuboid is 20 cm. Find the ratio of the bottom area of ??the cuboid to the bottom area of ??the container.

5. Two bosses A and B purchased the goods at the same price. For a certain fashion, B purchases 1/5 more sets than A, and then A and B sell it at a profit price of 80 and 50 respectively. After both are sold out, A still gets a part more profit than B. This means Part of the profit is just enough for him to purchase 10 more sets of this fashion. How many sets of this fashion did A originally purchase?

6. There are two water pipes A and B. They fill two pools A and B with the same size at the same time. The ratio of the water filling amounts of pipes A and B at the same time is 7:5. After 2 1/3 hours, the sum of the water injected into pool A and pool B is exactly one pool. At this time, the water injection speed of pipe A increases by 25, and the water injection speed of pipe B remains unchanged. Then, when pipe A fills pool A, When, how many more hours will it take for pipe B to fill pool B?

7. Xiao Ming walked from home to school in the morning. When he was halfway through the journey, his father found that Xiao Ming’s math book was left at home. He immediately rode his bike to deliver the book to Xiao Ming. When he caught up, Xiao Ming still had 3 /10 Before the journey was completed, Xiao Ming immediately got into his father's car and was sent to school by his father. In this way, Xiao Ming arrived at school 5 minutes earlier than walking alone. How long does it take for Xiao Ming to walk from home to school?

8. Both cars A and B start from place A and drive to place C through place B. The distance between places A and B is equal to the distance between places B and C. The speed of car B is car A. The speed is 80. It is known that car B started 11 minutes earlier than car A, but stayed at place B for 7 minutes, while car A kept driving to place C. Finally, car B arrived at place C 4 minutes later than car A. Then A few minutes after vehicle B set off, vehicle A overtook vehicle B.

9. Two cleaning vehicles, A and B, performed the task of cleaning the highway between the east and west cities. It took vehicle A 10 hours to clean alone, and vehicle B alone took 10 hours to clean. It takes 15 hours for a car to clean alone. The two cars drive toward each other from the east and west cities at the same time. When they meet, car A cleans 12 kilometers farther than car B. How many kilometers are there between the east and west cities?

10. Today there are 4 containers weighing 3 tons, 5 containers weighing 2.5 tons, 14 containers weighing 1.5 tons, and 7 containers weighing 1 ton. Then the minimum required How many trucks with a load capacity of 4.5 tons can be used to transport the container all at once?

Comprehensive training of primary school mathematics application questions (02)

11. The master and the apprentice both processed 170 parts. The master processed 1/3 of the number of parts compared to the apprentice. There are 10 more parts than 1/4, so how many parts did the apprentice process in one go?

12. A large car and a small car are both driving from point A to point B. The speed of the big car is 80 times the speed of the small car. It is known that the big car leaves 17 minutes earlier than the small car. But it stopped for 5 minutes at the midpoint between the two places before continuing to drive to place B; and the car did not stop halfway after setting off.

Then drive to place B. In the end, the small car arrived at place B 4 minutes earlier than the big car. We also know that the big car departed from place A at 10 a.m. So when did the small car catch up with the big car in the morning?

13. A manuscript takes 14 hours to complete by A typing alone, and 20 hours by B typing alone. If A types first for 1 hour, then B takes over from A to type for 1 hour, and then A takes over from B to type for 1 hour. Hours... The two of them worked alternately in this way. So how many hours did A and B spend on typing the manuscript?

14. 3 yellow balloons cost 2 yuan, and 2 flower balloons cost 3 yuan. The school *** bought 32 balloons, of which the flower balloons were 4 less than the yellow balloons. What kind of balloons did the school buy? How much money?

15. The speed of a sailboat is 60 meters/min. The boat is in a river with a current speed of 20 meters/min. It travels from a port upstream to a place downstream, and then returns to the original place. ***How ??many meters did the boat travel from the upstream port to a downstream location in 3 hours and 30 minutes?

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, then after granary A is full, the remaining flour in granary B will account for B. 1/2 of the capacity of granary A; if the flour from granary A is loaded into granary B, then after granary B is full, the remaining flour in granary A will account for 1/3 of the capacity of granary A. How many tons of flour can each granary hold? ?

17. Divide the number A by the number B, and divide the number B by the number C. The quotients are equal and the remainders are both 2. The sum of the two numbers A and B is 478. Then the sum of the three numbers A, B and C How much is it?

18. A car drives from point A to point B. If the speed is reduced by 10, it will arrive 1 hour later than the original time. If it travels 180 kilometers at the original speed, the speed will be increased. 20, then we can arrive 1 hour earlier than the scheduled time. How many kilometers is the distance between A and B?

19. A school participates in a military training queue performance competition and organizes a square team. If there are 60 people in each class, this square team must have at least 4 classes participating. If there are 70 people in each class, this square team The formation must have at least three classes of students participating. So how many people should make up this square formation?

20. Three lathes A, B, and C process square and round parts. It is known that 2 out of 3 parts processed by lathe A are round; lathe B processes 4 out of 4 parts each time. 3 out of 5 parts are round; 4 out of 5 parts processed by lathe C are round. On this day, the three lathes processed 58 round parts, and the number of square parts processed The ratio is 4:3:3, so how many parts can be processed by the three lathes today?

Comprehensive training of primary school mathematics application questions (03)

21. The circle of metal wire is 30 meters long. Cut out 3 metal wires of length A and 5 metal wires of length B. , if two more metal wires with length B are cut out from the remaining metal wire, there is still a difference of 0.4 meters. If two more metal wires with length A are cut out, there is still a difference of 2 meters. How many meters is the length of A?

22. A company wants to transport two kinds of building materials A and B to the construction site. Each piece of building materials A weighs 700 kilograms, and there are 120 pieces. Each piece of building materials B weighs 900 kilograms. ***There are 80 pieces. It is known that a car can carry up to 4 tons at a time. So how many times must 5 identical cars be transported at the same time?

23. The distance from Wang Li’s home to school is 1/4 longer than the distance to the gymnasium. One day, Wang Li took 17 minutes to walk home after watching a football match in the gymnasium. After a short rest, he walked again If you walk to school in 25 minutes, the speed is 15 meters per minute slower than when you come back from the gym. How many meters is the distance from Wang Li's home to school?

24. When a master and apprentice work together to complete a project, due to good cooperation, the master's work efficiency is 1/10 higher than when working alone, and the apprentice's work efficiency is 1/5 higher than when working alone. The two worked together for 6 days and completed 2/5 of the entire project. Then the apprentice worked alone for another 6 days. At this time, the project was still 13/30 unfinished. If the project was completed by the master alone, how many days would it take to complete it?

25. Students from five classes of sixth grade ***planted trees 1

00 trees. It is known that the number of trees planted by each class is different, and the ranking from most to least is exactly class one, two, three, four, and five. It is also known that the number of trees planted by one class is two and three The total number of trees planted by the second class is the sum of the number of trees planted by the fourth and fifth classes. So what is the maximum number of trees planted by the third class?

26. A ran 13 kilometers per hour, and B ran 11 kilometers per hour. B ran 20 minutes longer than A. As a result, B ran 2 kilometers more than A. B’s total *** How many kilometers did you run?

27. There are two cylindrical containers A and B with equal heights. The inner opening radii are 6 cm and 8 cm respectively. Container A is filled with water and container B is empty. Put container A in Pour all the water into container B. The depth of water in container B is measured to be 2 cm lower than 7/8 of the height of the container. What is the height of the container in cm?

28. There are 104 tons of goods, which are transported by a car with a load of 9 tons. It is known that the car takes 1 hour for each round trip. In fact, the car loads 1 more ton each time, so how many hours can be advanced Completed.

29. The master and the apprentice processed 225 parts on the first day. On the second day, they adopted a new process. The master processed 24 more parts than the first day, and the apprentice increased the number of parts. 45. Two people worked together to process 300 parts. How many parts did the master process the next day? How many parts did the apprentice process?

30. Fendou Primary School organized sixth-grade students to go to Baihua Mountain for camping and training. The distance increased by 2 kilometers every day. It took 4 days to go and 3 days to come back. I asked how far it is from the school to Baihua Mountain. rice?

Comprehensive training of primary school mathematics application questions (04)

31. The standard for charging electricity bills in a certain place is: the monthly electricity consumption does not exceed 50 kilowatt hours, and each kilowatt hour charges 5 cents; if If it exceeds 50 kilowatt-hours, the excess amount will be charged at 8 cents per kilowatt-hour. Each month, user A pays 3 yuan and 30 cents more for electricity than user B. How many kilowatt-hours of electricity did A and B each use this month?

32. Master Wang planned to process a batch of parts in 2 hours. When there were 160 parts left, the machine broke down and the efficiency was reduced by 1/5. As a result, the task was completed 20 minutes later than the original plan. How many parts are there in this batch?

33. Mom gave Honghong some money to buy New Year’s cards. There are three types of New Year’s cards: A, B, and C. Type A cards cost 1.20 yuan each. It’s more expensive to use the money to buy Type A cards than to buy them. There are 8 more cards of type B. If you buy a card of type B, you can buy 6 more cards than if you buy a card of type C. How much did mother give Honghong? How much does each type B card cost?

34. An old man had five sons and three houses. Before his death, he made a will and gave three houses to each of his three sons. As compensation, the three sons were allocated the house. Each person took out 1,200 yuan and divided it equally between the two sons who did not receive a house. Everyone said that this distribution was fair and reasonable. So how much is the value of each house?

35. Both Xiao Ming and Xiao Yan have less than 20 picture albums. If Xiao Ming gives Xiao Yan A copy, then Xiao Ming’s picture album will be twice as many as Xiaoyan’s; if Xiao Yan gives Xiao Ming A copy, then Xiao Ming’s The picture album is three times that of Xiaoyan. How many picture albums do Xiaoming and Xiaoyan have?

36. There are 160 red, yellow, and white balls. If you take out 1/3 of the red ball, 1/4 of the yellow ball, and 1/5 of the white ball, there will be 120 left. If you take out 1/5 of the red ball, 1/4 of the yellow ball, and 1/3 of the white ball, there will be 116 left. Question (1) How many original yellow balls are there? (2) How many original red balls and white balls are there?

37. The sum of the current ages of the father, brother and sister is 64 years old. When the father’s age is 3 times the brother’s age, the sister is 9 years old. When the brother’s age is 2 times the sister’s age At that time, my father was 34 years old. How old are the three of them now?

38. B is between A and C. A goes from B to A to deliver a letter. 10 minutes after departure, B sets off from B to deliver another letter. 10 minutes after B’s departure Minutes later, C discovered that A and B had just held the two letters upside down, so he rode from B to catch up with A and B in order to transfer the letters. It is known that the speeds of A and B are equal, and the speeds of C are If the speed is 3 times, how long will it take C from departure to return to B after transferring the message?

39.

There are 94 workers in workshops A and B. They process 1,998 bamboo chairs every day. Due to differences in equipment and technology, each worker in workshop A can only produce 15 bamboo chairs per day on average, while workshop B can only produce 15 bamboo chairs per day on average. A worker can produce 43 bamboo chairs per day. How many more bamboo chairs does workshop A produce per day than workshop B?

40. It takes A 10 minutes to walk home from school, and B 14 minutes to walk home from school. It is known that the distance traveled by B to go home is 1/6 longer than the distance traveled by A, and A’s distance per minute is longer than that of B. If you walk 12 meters more, how many meters does it take for B to go home?

Comprehensive training of primary school mathematics application questions (05)

41. The cost of each piece of a certain product is 72 yuan. It was originally sold according to the fixed price. 100 pieces can be sold every day, and the profit of each piece is the cost. 25, and then sold it at the price of 90, and the daily sales volume increased to 2.5 times the original. Based on this calculation, how many yuan does the daily profit increase from the original?

42. The speed ratio of trains A and B is 5:4. Train B starts first and drives from station B to station A. When it reaches a distance of 72 kilometers from station B, train A The train departs from station A to station B. The ratio of the distance between the place where the two trains meet and the distance between station A and station B is 3:4. Then how many kilometers is the distance between station A and station B?

43. There are ***35 big and small monkeys, and they go to pick peaches together. When the monkey king is not around, a big monkey can pick 15 kilograms in an hour, and a small monkey can pick peaches in an hour. Picking 11 kilograms. When the monkey king was on hand to supervise, each monkey, regardless of size, could pick 12 kilograms per hour. One day, picking took 8 hours, of which only the first hour and the last hour were supervised by the monkey king. The result was *** Picking 4,400 kilograms of peaches. How many little monkeys are there in this monkey group?

44. There are first and second prizes in a certain mathematics competition. It is known that (1) the ratio of the number of winners in schools A and B is 6:5. (2) Schools A and B will win the second prize in the coming year. The total number of first-class prizewinners accounts for 60 of the total number of prizewinners in the two schools. (3) The ratio of the number of second-class prizewinners in school A and B is 5:6. The number of second-class prizewinners in school A accounts for the total number of prizewinners in school A. What is the percentage of ?

45. It is known that the walking speed ratio of Xiao Ming and Xiao Qiang is 2:3, and the walking speed ratio of Xiao Qiang and Xiao Gang is 4:5. It is known that Xiao Gang walks 420 meters more than Xiao Ming in 10 minutes, then How many meters less did Xiao Ming walk than Xiao Qiang in 20 minutes?

46. To process a batch of parts, the original plan was to process 15 parts per day, which could be completed in several days. When 3/5 of the processing task was completed, new technology was used, and the efficiency increased by 20. As a result, the time to complete the task 10 days in advance, how many parts are there in this batch?

47. Two people A and B compete in a 10,000-meter race on a 400-meter circular track. They start from the starting point at the same time and in the same direction. At the beginning, A's speed is 8 meters/second, and B's speed is 8 meters/second. is 6 meters/second. When A catches up with B each time, A's speed decreases by 2 meters per second, and B's speed decreases by 0.5 meters per second. This continues until A finds that B catches up with him from behind for the first time. Both people increase their speed by 0.5 meters per second until the finish line. So when the leader reaches the finish line, how many meters away is the other person from the finish line?

48. Xiao Ming goes from home to school. If he walks 1.5 kilometers more per hour than before, he will only need 4/5 of the original time to walk this distance; if he walks 1.5 kilometers less per hour than before Kilometers, then how much longer does it take him to walk this distance than the original time?

49. The sum of the current ages of A, B, C and D is 64 years. When A was 21 years old, B was 17 years old; when A was 18 years old, C’s age was three times that of D. D’s current age How old are you?

50. Processing a batch of parts, the original plan was to process 30 pieces per day. When 1/3 was processed, due to improved technology, the work efficiency increased by 10, and the task was completed 4 days ahead of schedule. Question: How many parts are there in the batch?

Comprehensive training of primary school mathematics application questions (06)

51. The escalator moves upward at a uniform speed. A boy and a girl walk up the escalator at the same time. The boy’s speed is 2 times as long as the girl, it is known that the boy walked 27 steps to reach the top of the escalator, while the girl walked

I took 18 steps to reach the top. How many steps are there in the exposed part of the escalator?

52. Two piles of apples weigh the same. The first pile sells 2/3 and the second pile sells 50 kilograms. If there are fewer apples left in the first pile than in the second pile, So how many kilograms are there in the remaining two piles of apples?

53. Two cars A and B start from place A at the same time and drive back and forth between places A and B. It is known that the speed of car A is faster than that of car B, and after the two cars set off The first and second encounters were at point C on the road. How many times is the speed of car A than car B?

54. It takes *** 2 hours for a small boat to go back and forth from point A to point B. When it comes back, it follows the current and travels 8 kilometers per hour more than when it left. Therefore, the second hour is faster than the second hour. Travel 6 kilometers in one hour. Find the distance between places A and B.

55. Two cars, A and B, depart from places A and B respectively, and continuously travel back and forth between places A and B. Driving. It is known that the speed of car A is 15 kilometers/hour, and the difference between the third meeting point and the fourth meeting place of two cars A and B is 100 kilometers. Find the distance between A and B.

56. It took a person 7 minutes and 30 seconds to go from the top to the bottom along the upward moving escalator, and it only took 1 minute and 30 seconds for him to walk along the escalator from the bottom up to the top. If the person did not walk , so how long does it take to ride the escalator from bottom to top? If there is a power outage, how long will it take for this person to walk from the bottom to the top of the escalator?

57. Two cylindrical containers A and B have a bottom area ratio of 5:3. The water depth in container A is 20 cm, and the water depth in container B is 10 cm. Then pour the same amount of water into the two containers, Make the water depth in the two containers equal. How many centimeters is the water depth at this time?

58. A and B are 207 kilometers apart. Two cars, A and B, depart from A to B at the same time at 8:00, with speeds of 60 km/h and 54 km/h respectively. , Car C sets off from point B to point A at 8:30, with a speed of 48 kilometers/hour. What time will it be when the distance between car C and cars A and B is equal?

59. The perimeter of a rectangle is 130 cm. If its width increases by 1/5 and its length decreases by 1/8, a new rectangle with the same perimeter will be obtained. Find the area of ??the original rectangle.

60. There is a rectangle, the ratio of its length to width is 5:2, and the diagonal is 29 cm long. Find the area of ??this rectangle.

Comprehensive training of primary school mathematics application questions ( 07)

61. There is an orchard. Last year, there were 60 more fruit trees than fruit trees that did not bear fruit. This year, there were 160 more fruit trees. 5 times the number of fruit trees. How many fruit trees are there in the orchard?

62. Xiao Ming set off from point A to point B on foot, and Li Gang rode a motorcycle from point B to point A at the same time. The two met after 48 minutes. After arriving at point A, Li Gang immediately returned to point B. Catching up with Xiao Ming 16 minutes after the first encounter. If Li Gang kept traveling between places A and B, then when Xiao Ming arrived at place B, how many times did Li Gang catch up with Xiao Ming?

63. For the same walk of 100 meters, Xiao Ming has to walk 180 steps and his father has to walk 120 steps. The father and son start from the same place in the same direction at the same time. If each step takes the same time, then after the father walks 450 meters Go back, how many steps do you have to take before you meet Xiao Ming?

64. A ship sails between two ports. The water speed is 6 kilometers/hour. It takes 4 hours to sail with the current and 7 hours to sail against the current. Find the distance between the two ports.

65. There are three cars A, B and C, each driving from point A to point B at a certain speed. B starts 10 minutes later than C and catches up with C 40 minutes after departure; A beats B He sets off 10 minutes later and catches up with C 60 minutes after departure. How many minutes after departure does A catch up with B?

66. A and B cooperate to complete a task. Due to good cooperation, A's work efficiency is 1/10 higher than when they work alone, and B's work efficiency is 1/5 higher than when they work alone. B and B worked together to complete the work in 6 hours. If it took A 11 hours to do it alone, how many hours did it take B to do it alone?

6

7. Five students A, B, C, D, and E stand in a row, holding 20 small flags in their hands. Now we know that the student standing to the right of C holds 11 small flags. , the student *** standing to the left of B is holding 10 small flags, the student *** standing to the left of D is holding 8 small flags, and the student *** standing to the left of E is holding 16 small flags. Five Who are the students from left to right? How many small flags do you get each?

68. Xiao Ming ran a lap on a 360-meter-long circular track. It is known that he ran 5 meters per second in the first half of the time and 4 meters per second in the second half. Ask him about the distance in the second half. How long did it take?

69. In order to measure the length and speed of the train passing by, Xiaoying and Xiaoming took two stopwatches. Xiaoying used a watch to record the time it took for the train to pass in front of him as 15 Seconds, Xiao Ming used another watch to record the time it took from the front of the car to pass the first telephone pole to the rear of the car to pass the second telephone pole, which was 18 seconds. It is known that the distance between the two telephone poles is 60 meters. Find The total length and speed of the train.

70. When Xiao Ming goes from home to school, he walks for the first half of the distance and takes the car for the second half; /3 time walking. As a result, the time to go to school is 20 minutes longer than the time to go home. It is known that how many kilometers is Xiao Ming’s distance from home to school?

Comprehensive training of primary school mathematics application questions (08)

71. Mathematics exercises were held 20 times, and 374 test questions were asked. The number of questions each time was How many times have questions 16, 21, and 24 been asked respectively?

72. If an integer is divided by 2, the remainder is 1. Divide the obtained quotient by 5, leaving a remainder of 4. Then divide the obtained quotient by 6, leaving a remainder of 1. Divide this integer by 60, what is the remainder?

73. The young pioneers planted twice as many apple saplings as pear saplings on campus. If each person planted 3 pear saplings, there would be 2 more; if each person planted 7 apple saplings, there would be less 6. How many young pioneers does *** have? How many apple and pear saplings are there?

74. A person drives a car 200 kilometers from city A to city B. At the beginning, he drove at a speed of 56 kilometers per hour, but the car broke down and it took half an hour to stop for repairs. In order to arrive on time, he must increase his speed by 14 kilometers/hour. After running the next distance, how many kilometers away from city A is the place where he repairs his car?

75. Two people A and B start from places A and B at the same time and go towards each other. B's speed is 2/3 of A. After they meet, they continue to move forward. A arrives at place B. B returns immediately after arriving at A. It is known that the place where the two met for the second time is 3000 meters away from the place where they first met. Find the distance between A and B.

76. A boat goes back and forth between Between ports A and B, it is known that the speed of the ship in still water is 9 kilometers/hour. The ratio of the time spent in normal retrograde and forward movement is 2:1. One day it rained, and the speed of the water was doubled. This boat takes 10 hours to go to and from ***. How many kilometers are there between ports A and B?

77. The entrance examination of a certain school determined the admission score. Only 1/3 of the students who applied for the exam were admitted. The average score of the admitted students was 6 points higher than the admission score. The average score of the students who were not admitted was It is 15 points lower than the admission score. The average score of all candidates is 80 points. What is the admission score?

78. A group of students move bricks. If there are 12 people each moving 7 bricks, and the rest each move 5 bricks, then there will be 148 bricks left in the end; if there are 30 people each moving 8 bricks, The remaining people each moved 7 yuan, so there are 20 yuan left at the end. Ask the students how many people are there? How many bricks are there?

79. Two cars A and B are traveling towards each other at the same time from places A and B respectively. It is known that the ratio of the speed of car A to the speed of car B is 4:3, and place C is between A and B. , the time when two cars A and B arrived at location C were 8 a.m. and 3 p.m. respectively. What time did cars A and B meet?

80. In a chess match, the scoring method is as follows: the winner gets 2 points, the loser gets 0 points, and both players in a draw get 1 point each. Each player plays against the other players once. Now we know the male of the contestants

There are 10 times more students than girls, but their total score is only 4.5 times that of girls. How many girls are participating? What score does a girl get for ***?

Comprehensive training of primary school mathematics application questions (09)

81. There are several natural numbers, and their arithmetic mean is 10. If the largest one is removed from these numbers, the remaining The arithmetic mean of is 9; if the smallest one is removed, the remaining arithmetic mean is 11. What is the maximum number of these numbers? What is the maximum value of the largest number among these numbers?

82. There are 35 Young Pioneers in a class and 23 boys in this class. How many more female Young Pioneers are there than male non-Young Pioneers in this class?

83. Xiaodong plans to visit the ape-man ruins in Zhoukoudian. If he travels by car at a speed of 40 kilometers/hour, he will arrive 3 hours earlier than by bicycle. If he travels at a speed of 8 kilometers/hour If we walk at the same speed, it will arrive 5 hours later than riding a bicycle. How many kilometers is it from Xiaodong’s starting point to Zhoukoudian?

84. Two boats A and B are sailing on a river 90 kilometers apart. If they go in opposite directions, they will meet each other in 3 hours. If they go in the same direction, boat A will catch up with boat B in 15 hours. Seek in silence The speed of boats A and B in the water.

85. There are 90 students in the two classes of the second grade, including 71 young pioneers. The young pioneers of the first class account for 75 of the class, and the young pioneers of the second grade The young pioneers of the class account for 5/6 of the class. How many more young pioneers are there in the first class than in the second class?

86. A container has been filled with water. There are three balls: large, medium and small. The first time the small ball is sunk into the water, the second time the small ball is taken out, and the middle ball is sunk into the water. , take out the middle ball for the third time, and sink the small ball and the big ball into the water together. Now we know that the amount of water overflowing from the container each time is: the first time is 1/2 of the second time, and the third time is 1/2 of the second time. 1.5 times the quadratic. Find the ratio of the volumes of the three balls.

87. It took a person 2 hours to climb a mountain and 2.5 hours to return. His speed going up the mountain is 3000 meters/hour. The speed of going down the mountain is 4500 meters/hour. How many meters does it take to cross the mountain?

88. Each steel bar raw material is 7.3 meters long. Each set of steel bar racks uses a section of 2.4 meters, 2.1 meters and 1.5 meters long steel bars. Now it is necessary to tie 100 sets of steel bar racks, at least the raw materials must be used How many roots?

89. There is a piece of copper-zinc alloy, in which the ratio of copper to zinc is 2:3. It is now known that 6 grams of zinc are added, and after melting, 36 grams of new alloy are obtained. The copper and zinc in the new alloy are What's the ratio?

90. Xiao Ming usually walks to school. One day he wanted to exercise. He ran fast for the first 1/3 of the way, at a speed 4 times walking speed, and jogged the last part of the way, at a speed equal to walking speed. 2 times. If Xiao Ming arrives at school 35 minutes earlier than usual, how many minutes will it take Xiao Ming to walk to school?

Comprehensive training of primary school mathematics application questions (10)

91. There are three people, A, B and C. A’s age is 2 times and 3 years older than B’s. The age is 2 years younger than 2 times the age of C. The sum of the ages of the three people is 109 years. Find the ages of A, B and C respectively.

92. The express train travels at 60 km/h The local train departs from station A to station B. 1.5 hours later, the local train departs from station B to station A at a speed of 40 km/h. When the two trains meet, the meeting point is 70 kilometers away from the midpoint of the two stations. How many kilometers are there between stations A and B?

93. Cars A and B left the school one after another and drove to the museum at the same speed. It is known that the distance between car A and the school at 8:32 is three times the distance between car B and the school. At 8:39 The distance between car A and the school is twice the distance between car B and the school. Find the time when car A leaves the school.

94. There is a work group. When each worker is working at his or her job At , a batch of parts can be produced in 7 hours. If the positions of workers A and B are exchanged and the others remain unchanged, then this batch of parts can be completed 1 hour in advance. If the positions of workers C and D are exchanged and the others remain unchanged, it will also You can ask 1 hour in advance. If the positions of A and B, C and D are exchanged at the same time, and the other people remain unchanged, then this batch of parts will be completed.

How long does it take?

95. Use 10 rectangular volumes of 7 cm long, 5 cm wide and 3 cm high to form a cuboid. What is the minimum surface area of ??the cuboid?

96. Gongyuan only sells two types of tickets: individual tickets are 5 yuan each, and group tickets for 10 people are 30 yuan each. If you purchase more than 10 group tickets, you can get a discount of 10. (1 ) 45 people from unit A visit the park. If they buy tickets according to the above regulations, how much is the minimum amount they should pay? (2) If 208 people from unit B visit the park and buy tickets according to the above regulations, how much is the minimum amount they should pay?

97. A, B, and C take an exam and get 260 points. It is known that 1/3 of A’s score, 1/4 of B’s score and half of C’s score are subtracted 22 points are equal, so how much does C score?

98. For a project, A and B work together for 4 days, and then B completes it alone for 5 days. It is known that A completes 1/30 more of the project than B every day. A, How many days will it take B to do this project alone?

99. There are two candles, a long one and a short one (burning at the same length in the same time). The sum of their lengths is 56 cm. After they are lit at the same time for a period of time, the long candle is as long as the short candle before it is lit. , then the length of the short candle is exactly 2/3 of the long candle. How long is the long candle before it is lit?

100. A batch of apples are packed equally in 20 baskets. If each basket is filled with 1/9 more, how many baskets can be saved?

Comprehensive training of primary school mathematics application questions (11)

101. Xiao Ming bought a pen, and the money he spent was 0.5 yuan more than half of the total money he brought; he bought it For a ballpoint pen, the money spent is 0.5 yuan less than half of the money left after buying the pen; he bought a notebook for 2.8 yuan, and finally there was 0.8 yuan left. How many yuan did Xiao Ming bring?

102. The son is 6 years old this year. The father’s age 10 years ago is equal to the son’s age 20 years later. When the father’s age is exactly twice the son’s age, in which year AD?

103. On a 12-meter-long wire, a yellow beetle crawls from the right end to the left end at a speed of 15 centimeters per minute at 8:20; at 8:30, a red beetle and a blue beetle crawl from the left end at a speed of 15 centimeters per minute. Climbing to the right end at speeds of 13 centimeters and 11 centimeters per minute, at what moment does the red beetle happen to be in the middle of the blue beetle and the yellow beetle?

104. A People's Liberation Army unit drives from its base to a certain place for flood relief. If the vehicle speed is increased by 1/9 than the original, it can arrive 20 minutes before the scheduled time; if it drives at the original speed first 72 kilometers, and if the vehicle speed is increased by 1/3 than the original, we can arrive 30 minutes earlier than the scheduled time. How many kilometers does this People's Liberation Army unit travel?

105. A round trip from Pier A to Pier B takes 4 hours. When it comes back, it travels 12 kilometers per hour with the current than when it went out. Therefore, the last 2 hours are longer than the first 2 hours. If the line is 18 kilometers, then how many kilometers are the distance between terminals A and B?

106. The ratio of the number of students in Class A and Class B is 5:4. If 9 students are transferred from Class B, then Class A will have 2/3 more students than Class B. At this time How many people are there in Class B?

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