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Mathematical Olympiad in the Sixth Grade of Primary School
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1. A bag of flour, eaten 15 Jin, 5 Jin 2/5 more than that not eaten. How much does this bag of flour weigh?

2.50 kg of salt water containing 10% salt. How many kilograms of salt do you need to add now to increase its concentration to 20%?

3. There is a pile of conical wheat. The measured bottom circumference is12.56m and the height is1.5m.. How many meters can it hold in a cylindrical granary with a bottom diameter of 2 meters?

4. How many square meters of iron is needed to make a cylindrical iron drum with a bottom circumference of 18.84 decimeters and a height of 20 decimeters.

5. There is a cylindrical iron cylinder with a height of 10 cm and a bottom radius of 4 cm. What is the area attached to the side of the manual?

6. A cone-shaped sand pile with a height of 3m and a bottom circumference of 31.4m. If the sand weighs 1.5t per cubic meter, how many tons does this pile weigh?

7. Cast an iron block with a bottom area of 15.7 square decimeter and a height of 20 decimeter into a cone with a bottom radius of 5 decimeter. What is its height?

8. Processing a batch of parts can be completed in 20 hours if processing 120 pieces per hour, and how much should be processed per hour if processing 15 hours is required?

9. When a wire is cut 20 meters, its weight is 5 kilograms. At present, this line 1800 kg. What's its length?

10. It takes 450 bricks with an area of 9 square decimeters to pave a piece of land with bricks. If you use square bricks with an area of 25 square decimeters, how many bricks do you need?

1 1. A team of a coal mine mined for 3.5 hours 105 tons. According to this calculation, it will take 5.5 hours to mine. How many tons of coal has this team mined?

12. It takes 460 pieces to pave the floor with rectangular small wooden blocks with a length of 63 cm and a width of 40 cm. If you replace it with a small piece of wood with an area of 1 square decimeter, how many pieces do you need?

13. Two parallelograms A and B overlap, and the areas of overlapping parts are 1/4 of A and 1/6 of B respectively. Given that the area of A is 12 square centimeters, how many square centimeters is B more than the area of A? (Use proportional solution)

14. There are 56 students in Grade 4 in xinhua primary school, 3/7 of whom are boys. Later, I transferred a few boys. At this time, boys accounted for 7/ 15 of the class. How many boys have transferred to other schools?

15. A company plans 15 people to work 8 hours a day and complete a batch of orders in 6 days. Later, due to the urgent task, the company changed to 18 people to complete the order in 4 days. How many hours must they work every day?

16. Make a cuboid model with a line with a length of 108 cm, and the side length ratio is required to be 2: 3: 4. If each surface is wrapped with iron sheets to make an iron box, what is the volume of the iron box?

17. One meter-gauge train runs 68 kilometers per hour, and the other train runs 76 kilometers per hour. These two trains leave from Station A and bilibili at the same time. After 5/6 hours, they are still 1/4 of the length of the railway between the two stations. How long is the railway between Station A and bilibili?

18. Xiaoming and Xiao Liang each have some glass balls. Xiao Ming said, "Your balls are less than mine 1/4." Xiao Liang said, "If you can give me your 1/6, I will have two more than you!" How many original glass balls does Xiaoming have?

19. A factory produces a batch of cement, which was originally planned to produce 150 tons per day, and the task can be completed on time. Actually, the output was increased by 30 tons per day, and the task was completed in only 25 days. How many days does it take to complete the original planned production task?

20. To build a road, 2/5 of the total length was built on the first day, and 50% of the total length was built on the second day, leaving 3.2 kilometers to be repaired. How many kilometers is this road?

2 1. It takes six hours by car from city A to city B, and four hours from city B to city A ... Now two cars, A and B, start from two cities at the same time and travel relatively. When they met, the car that entered A traveled 96 kilometers. How far is the distance between a and b?

Answer:

1. Let the original value be x kg. The formula is: (X- 15)*2/5+5= 15, and X=40 is obtained.

2.50*20%-50* 10%=5 (kg)

3. Cone bottom radius = 12.56/∏/2=2 (m), cone volume = 22 * 3.14 *1.5 *1/3 = 6.28 (m3) cylinder.

4. lateral area = 18.84*20=376.8 (square decimeter) bottom radius = 18.84/3. 14/2=3 (decimeter) bottom area = 32 * 3.14.

5. Side area = 4 * 2 * 3.14 *10 = 251.2 (square centimeter).

6. The bottom radius =3 1.4/3. 14/2=5 (m) Volume = 5 2 * 3. 14 * 3 = 235.5 (m3), and the weight is 235.5 *1.

7. You didn't say what shape iron is! ! ! I have to work out the volume of iron 15.7*20=3 14 (square decimeter), the cone bottom area is 5 2 * 3.14 = 78.5 (square decimeter), and the height is 314 * 3/77.

8.120 * 20/15 =160 (piece)

9. 1800/5*20=7200 (m)

10.9*450/25= 162 (piece)

11.105/3.5 * (3.5+5.5) = 270 (ton)

12.63 * 40 * 460/100 =11776 (block)

13.12 * (1/4)/(1/6)-12 = 6 (square centimeter)

14. Let the transferred boys be X people. 56*(3/7)+X=(56+X)*(7/ 15) gives X=4.

15.15 * 8 * 6/(18 * 4) =10 (hour)

16. If the side length is 2k, 3k and 4k, then (2k+3k+4k)*4= 108, and the solution is k=3, then each side is 4, 6 and 8, and the volume is 4*6*8= 192 (cubic

17. What does "0/4 of the length of the railway between two stations after 65438+5/6 hours" mean? The distance between the two cars is 1/4 of the railway! I understand that (68+76) * (5/6)/(1-1/4) = 432 (km).

18. Let there be X Xiaoming. (1-1/4) * x+(1/6) * x-2 = (5/6) * x gives X=24.

19. (150+30) * 25/150 = 30 days.

20. Let the total length be x kilometers. (2/5)*X+50%*X=X-3.2, the solution is X=32.

2 1. let AB distance be x km. 96/(X/6)=(X-96)/(X/4) gives X=240.