The amount of water pumped includes constant water storage and daily water injection.
Suppose 1 water pump pumps 1 water a day, the former pumps 100 (5*20) and the latter pumps 90 (6* 15). Why does the latter pump less water 10? Because the river water has been injected for less than 5 days (20- 15), it is known that the river water can be injected with 2 portions of water every day (10/5). At this point, it can be calculated that the number of parts stored in the container is 60.
According to the meaning of the question, adding 12 river water (6*2), a total of 72 sets of water were pumped in 6 days, and 12 sets (72/6) were needed.
2. A man was standing by the railway, and it took 57 seconds for the train to pass in front of him after he heard the whistle of the through train. It is known that when the train whistles, it is 1360 meters away from him, and the speed of sound propagation in the air is 340 meters per second. Find the speed of the train.
It takes 1360/340=4 seconds for the sound to reach his ears, so the train actually runs at 57+4=6 1 360m, so the train speed is 1360/61m per second.
3. The sum of the ages of Party A, Party B and Party C is 1 13 years old. When Party A is half the age of Party B, Party C is 38 years old, and when Party B is half the age of Party C, Party A is 17 years old. Find the age of B.
Suppose that when A is half the age of B, A is one year old, B 2×A is old, and C 38 is old; When A is 17 years old, it is noted that the age difference between A and B is unchanged, so B is 17+a, so C is twice that of B, which is 2×( 17+a). According to the age difference between A and C, we can get: 38-A = 2× (65438+A). B is 14 years old, C is 38 years old, and the total is 7+ 14+38=59 years old, (113-59) ÷ 3 =18. In 18 years, the sum of their ages will be 60.
4. There is a refrigerator, the original price is 2000 yuan, and it is sold at a reduced price of 1600 yuan, which is a few percent lower?
(2000- 1600) ÷ 2000 = 20% A: 20% lower.
5. There is an air conditioner, the original price is 1600 yuan, but after the price increase, it sells for 2000 yuan, which is a few percent higher?
(2000-1600) ÷1600 = 25% A: It increased by 25%.
6. There is a TV with the original price of 1200 yuan, which is lower than that of 300 yuan. How much is the price reduction?
300 ÷ 1200 = 25% A: 25% lower.
7, there is a kind of disinfection cabinet, the original price is 2400 yuan, the price has increased by 400 yuan, and the price has increased by several percent.
400 ÷ 2400 ≈ 16.6% A: It has gone up 16.6%.
8. bright primary school had 24 basketballs last year and bought six new ones this year. How many basketballs are there today? What percentage has this year increased compared with last year?
24+6 = 30(a)30÷24 = 125% 125%- 100% = 25%。
9. The original ticket for a park in 80 yuan will be 20% off during the National Day. How much can you save per ticket? What's the equivalent of a price reduction?
80×0.8=64 yuan 80-64= 16 yuan.
(80-64) ÷ 80 = 20% A: It can save 16 yuan, which is equivalent to a price reduction of 20%.
10, Nanshan Primary School * * * covers an area of 8,000 square meters, of which the green area accounts for 65%, and the rest are teaching buildings and roads. What is the green area of Nanshan Primary School? How many square meters are there in the teaching building and road?
8000× 65% = 5200 (square meter) 8000-5200=2800 (square meter)
Answer: Nanshan Primary School has a green area of 5,200 square meters and 2,800 square meters of teaching buildings and roads.
1 1. Shopping malls offer discounts, 50% off clothing and 20% off stationery. How much does Xiao Ming actually spend on a dress with the original price of 320 yuan and a schoolbag with the original price of 120 yuan?
120×0.8+320×0.5=256 (yuan) A: Actually, it costs 352 yuan.
12. The germination rate of a batch of seeds is 98.5%. Sowing 3000 seeds, how many seeds may not germinate?
3000×( 1-0.985)=45 (grains) A: There may be 45 seeds that have not germinated.
13. Last year, an orchard produced 4500 kilograms of apples. This year, due to the good climate, the output has increased by 20% compared with last year. How many kilograms of apples have been produced this year?
4500×( 1+0.2)=5400 (kg) A: The output of apples this year is 5400 kg.
14, girls in the sixth grade of experimental primary school account for 48.75% of the whole grade, and what is the proportion of boys in the whole grade? If there are more boys than girls 12, how many are there in the sixth grade of experimental primary school?
1-48.75% = 51.25%12 ÷ (51.25%-48.75%) = 480 (person)
15. The vegetable base produced 24,000 tons of vegetables this year, an increase of 20% over last year. What was the output of this vegetable base last year?
2.4÷( 1+0.2)=2 (10,000 tons) A: The output of this vegetable base last year was 20,000 tons.
16. Generally, 7.8 yuan sells a marker in the store and earns 30%. Now it is sold at a reduced price in 6.2 yuan. Is it profit or loss? How much difference?
Solution: the cost of each pen is X. According to the meaning of the question, x( 1+30%)=7.8.
The solution is x=6 (yuan) and because it is sold in 6.2 yuan now, it earns 6.2-6=0.2 yuan.
17, physical education class, every 5 people jump rope, every 3 people throw sandbags, * * * 42 students took part in the activity. How many people took part in skipping rope and throwing sandbags? (do it by arithmetic)
42/5=8 Yu 2=7 Yu 7=6 Yu 12=5 Yu 17=4 Yu 22=3 Yu 27=2 Yu 32= 1 Yu 37.
So six groups of skipping rope, four groups of throwing sandbags, or three groups of skipping rope and nine groups of throwing sandbags can meet the problem. 5 * 6 = 30 3 * 4 = 12 or 5 * 3 = 15 3 * 9 = 27 There are 30 people who jump rope and throw sandbags, and there are 12 people alive, 15 and 27 people.
18, 0.40 yuan for exercise books and 0.32 yuan for pencils. The teacher asked Xiaohu to buy some exercise books and pencils, and the total price was exactly given by the teacher 10 yuan. But the tiger confused the number of exercise books with the number of pencils and got back 0.56 yuan. So the teacher originally planned to let Tiger buy basic exercise books?
Suppose I have to buy X exercise books and Y pencils.
Equation set 0.4x+0.32y =100.4y+0.32x = 9.44.
X= 17 y= 10 The teacher originally planned to let Xiaohu buy 17 exercise books.
/kloc-Grade 0/9/6 students went boating in the park. If each boat takes 10 people, there will be two more seats. If there are two more people on each boat, you can rent 1 boat less. So, how many boats does * * * need to rent?
Assuming that each ship needs to rent x ships with 10 people, then each ship needs to rent x-12 people, and the equation is obtained.
10x-2 = 12(x- 1)- 12
The solution is x=5.
Therefore, each boat needs to rent 5 boats for 10 and 4 boats for 12.
20, comprehensive knowledge to answer questions, answer a question plus 10, answer 1 4 points.
(1) A student * * * answered 10, and finally got 72 points. He answered several questions correctly.
(2) Student B * * * answered the question 12, and finally got 22 points. He answered several questions correctly.
( 1) 10 * 10 = 100(min) 100-72 = 28(min)28 \( 10+4)= 2(Dao)65438。
A: Eight correct answers.
(2) 12 * 10 = 120(min) 120-22 = 98(min)98 \( 10+4)= 7(Dao) 12-。
A: Five correct answers.
2 1. Xiaoming has 40 triangular, rectangular and pentagonal cards. These cards have 156 corners, of which the number of rectangles and pentagons is the same. How many cards are there in each of the three cards?
Solution: Let a rectangle and a Pentagon have X triangles and (40-2x) triangles respectively (because the number of rectangles and pentagons is the same, one is X and the other is X).
5x+4x+(40-2x)×3= 156
9x+ 120-6x= 156
3x+ 120= 156
x= 12
The number of rectangles and pentagons is the same, with 12 triangles and 16 triangles respectively.
22. Party A and Party B have a total of *** 1 10 items. If Party A gives Party B 20 items, the ratio of the number of items of Party A and Party B is 6:5. How many items did Party A and Party B originally have?
6+5= 1 1
A original:110× 6/11+20 = 80.
B original: 1 10-80=30.
23. Four brothers want to buy a boat in partnership. The money paid by the eldest is 1 of the other three, the money paid by the second is 1 of the other three, the money paid by the third is 1 of the third, and the fourth is 80,000. How much is this boat worth?
This problem seems difficult to teach, but it is actually quite easy. Chairman Mao once said that "all reactionaries are paper tigers". Let's beat the paper tiger together! Using the idea of integer, the score in the problem is regarded as a ratio, that is, the ratio of the boss to the other three people is 1: 3, so the boss accounts for a quarter of the total. Similarly, the second child accounts for one sixth and the third child accounts for one third. This becomes the simplest problem of score application, and then consider the corresponding relationship between the actual quantity and the score rate. 8÷( 1- 1/4- 1/6- 1/3)=32
24, a barrel of oil, the first time poured out two 5 kilograms, the second time poured out three 8 kilograms, and twice just poured out a quarter of the barrel of oil. How many kilograms is this barrel of oil?
2/5+3/8=3 1/40; (31/40)/(1/4) = 3.1(kg)
25. It took an engineering team two months to complete a 4000-meter-long road, of which the second month was equivalent to two thirds of the first month. How many meters are repaired every month?
1+3/2=5/2
Repair 4000 *1(5/2) = 4000 * 2/5 =1600 meters in the first month.
Repair 4000*(3/2)/(5/2)=4000*3/5=2400 meters in the second month.
26. What is the difference between a quarter minus the product of a fifth and six fifths and eight fifths?
( 1/4- 1/5)*5/6= 1/24 ( 1/24)/(5/8)= 1/24*8/5= 1/ 15
27, 32 is more than 20 ()%, and 20 is less than 35 ()%.
(32-20)/20* 100%=60% (35-20)/35* 100%=42.9%
28. The sum of the sides of a cuboid is 80 cm, and the ratio of length to width to height is 5: 3: 2. The volume of this rectangle is () cubic centimeters.
If the sum of the sides of a cuboid is 80 cm, then length+width+height =80/4=20 cm.
5x+3x+2x=20
10x=20
x=2
The length, width and height are 10, 6 and 4 cm respectively. Therefore, volume = length * width * height = 10*6*4=240 cubic centimeters.
29. There is a wooden house on the grassland. The wooden house is a square with a side length of 3 meters. A is a corner of the wooden house. There is a stake at point A. A horse is tied to the stake with a 6-meter-long rope. What is the range of this horse?
Draw a picture to understand it faster. 6 * π * three-quarters square: three-quarters of the area of a circle with point A as the center and 6 meters as the radius. The square of 3 times π divided by four times two: The picture shows the area of horses on both sides of the wooden house (the side with point A).
30. "The fruit shop sells two kinds of fruits, and after the watermelons bought with 2000 yuan are sold out, it earns 20%. Because of poor storage, strawberries only sold for 2000 yuan, a loss of 25%. Are these two fruits generally lost or gained? Can you tell me the reason? "
The total cost of selling watermelons is 2000*0.2+2000=2400. The other total cost is 2000/0.75=2666.7.
3 1 Grade 6 students are divided into interest groups. There are 5 people in the science and technology group, 3 people in the art group, and 37 people signed up, which is exactly divided into 9 groups. How many people are there in the science and technology group and the art group?
Assuming it's all art.
3x9=27
37-27= 10
Science and technology 10 divided by (5-3)=5 groups 5x5=25 people.
Article 9-5 =4 groups 4x3= 12 people.
32. The ratio of the number of plows and baskets of apples brought in by the fruit shop is 3:2. When only 15 basket plough is sold, the number of apples accounts for 4/5 of the plough. How many baskets of pears and apples are there now?
Solution: Set each X basket.
2x:(3x- 15)=4:5
10x= 12x-60
2x=60
x=30
Originally: pears: 3*30=90 baskets, apples: 2*30=60 baskets.
Now: pears: 90- 15=75 baskets, apples: 2*30=60 baskets.
At the beginning of this semester, the ratio of girls to the whole grade was 5: 8. After five girls transfer, the ratio to the total number of students in the whole grade is 16: 25. How many people are there in the whole grade now?
Because the number of men remains the same, we can know that the ratio of the number of boys to the number of students in the whole school is (8-5): 8 = 3: 8.
After the transfer, it is (25- 16): 25 = 9: 25.
3:8=9:24
So 25-24= 1 copy, just five people transferred it. So the number of students in the whole grade is 5*25= 125.
34. There are 65,438+0 yuan, 5 yuan and 65,438+00 RMB * * 65,438+04, 1 * * 66 yuan, of which 65,438+0 yuan has two RMB more than 65,438+00. How much RMB do these three kinds have?
Solution: Assuming one yuan RMB X, then 10 yuan RMB (x-2), 5 yuan's (14-x-x+2)=( 16-2x),10 (x-2)+5 (.
x=6
Answer: 1 yuan 6, 5 yuan 4, 10 yuan 4.
35. There are 137 sheep in two pastures. If Ranch A sells 25% and Ranch B buys 3 sheep, then the number of sheep in the two pastures is exactly equal. How many cotton sheep are there in those two pastures?
Solution: If A's pasture has X and B has (137-x),
( 1-25%)x=( 137-x)+3
x=80
A: There are 80 sheep in Ranch A and 57 sheep in Ranch B. ..
36. The department store sold two kinds of goods, each of which won the 300 yuan. One of them made 20% and the other lost 20%. Did this store make a profit or lose money by selling these two commodities? (Solution of formula)
The cost of profitable goods is: 300 ÷ (1+20%) = the cost of loss-making goods in 250 yuan is: 300÷( 1-20%)=375 yuan, so the total cost is: 375+250=625 yuan > 600 yuan.
So the store lost money.
37. The length, speed and height of a cuboid block are 8 cm, 5 cm and 4 cm respectively. If you saw it into the largest cube, how much smaller would it be? (Solution of formula)
The volume of the original cuboid is 8×5×4= 160 cubic centimeter.
The maximum side length of a cube is 4 cm, and its volume is 4×4×4=64 cubic centimeters.
So the percentage of volume reduction is: (160-64)/160×100% = 60%.
38. If the overlapping areas of two semicircles with different sizes are respectively equivalent to 2/7 of the small semicircle and 2/9 of the large semicircle, the area ratio of the large semicircle and the small semicircle is ().
9:7
39.a and B are 600 kilometers apart. Car dealers need 10 hours to complete the journey. The speed of a car is 125% of that of a car. If A and B start at the same time, how many hours will they meet?
A car speed: 600/19 = 60 km; B speed: 60x 125% = 75km.
600/(60+75)=4 and 4/9=40/9 hours
40. The sixth-grade students in a school go to the movies in two cars. At first, there were six more people in car A than car B. Later, the teacher transferred 15 people from car A to car B. At this time, the number of people in car A was 5/8 of that in car B. How many people are there in car B now?
(15+ 15-6)/3*8=64 (person)
A: Now there are 64 people on the B train.
4 1, and the speed ratio of Party A and Party B is 3: 2. They set out from A and B at the same time, and walked in opposite directions, and met on the road after 12 minutes. How many minutes does it take for B to walk to A?
Because the speed ratio of Party A and Party B is 3: 2, it takes the same time to meet each other.
So the distance ratio when A and B meet is 3: 2. So it takes 12/2*3= 18 (point) to get from B to A.
A: it takes 18 minutes for b to walk to a.
42. The diameter of a car wheel is 0.5 meters. How many times does the wheel turn when the car travels to 1 km?
If the diameter of an automobile wheel is 0.5m, the circumference of the wheel is 0.5π≈ 1.57 (m).
Garage 100m, wheel rotation 1000÷ 1.57≈64 (circle).
43. The fence of a gymnasium is circular, and it goes around the fence, with 628 steps, each of which is about 0.6 meters long. How many square meters does this gymnasium cover?
The circumference of the gymnasium is 628×0.6=376.8 (m).
Then the radius of the gymnasium = 376.8÷2≈60 (meters).
The area of the gymnasium is equal to 60×60×π≈942 (square meters).
44. For a box of goods, take out 168 pieces first, and then take out the remaining 2/3, so the remaining box is exactly 1/7 of the total number of pieces. How many pieces of goods are there in this box?
1/7 ÷ (1-2/3) = 3/7 * *:168 ÷ (1-3/7) = 294 (pieces)
45. Team A takes 6 days, Team B takes 8 days and Team C 12 days to complete a project. How many days does it take for three teams to work together to complete three-quarters of the project?
1\ (1\ 6+1\ 8+1\12) x3 \ 4 = 2 (days)
46. The sales of a computer company this year is 6.5438+0.8 million yuan, an increase of 20% over last year. How many billion yuan has this year increased compared with last year?
Solution: Suppose last year's sales were X million yuan.
X+20%X= 180
X= 150
180- 150=30 (ten thousand yuan)
47. A piece of iron and copper alloy, of which 27 Jin is iron, find the copper content of this alloy.
The atomic mass of iron is 56, and that of copper is 64.
Copper inlaid x gold
27/56=x/64
x≈30.86
Copper content =30.86/30.86+27≈53.33%
48. The circumference of a rectangle is 88 cm, and the ratio of length to width is 7: 4. How many centimeters is the length and width of a rectangle? What is the area of 9 square meters?
The sum of length and width is: 88/2=44 cm.
7+4= 1 1 has a length of 44 * 7/1= 28 cm and a width of 44 * 4/1=16 cm.
Area: 28* 16=448 square centimeters.
49. In a round vegetable field (r= 10m), Xiaohong's mother planted vegetables and radishes in a ratio of 2: 3. How many square meters of vegetables does Xiaohong's mother grow?
10×2/5=4 square meters
50. The ratio of girls to boys in Class 6 (2) is 4: 5. I recently transferred 1 girl. At this time, the number of girls is five-sixths of that of boys. How many people are in the class now?
There are ***X people in the class, so 5x/1-1= 4 (x-1)/9 calculates X=55.