Reason + percentages - math problems

Number of problems found: 84

Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice
Beer tapping
When checking compliance with the beer tapping, it was found that 60% of the offered beers were underfilled. The others were fine. Thus, instead of 0.5 l, the volume was 4.4 dcl on average. What was the volume of one average underfilled beer?
Birthday paradox
How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
The manufacturer
The manufacturer found that 3% of the plates produced had a malfunction. Of the compliant, 75% are first and 25% second. What is the probability of producing first and second class plates?
The test
The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
Alarm systems
What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
Students
If the fifth-grade class left 20% of students and in the seventh grade were added two pupils, in the eighth one pupil, the number has not changed in the ninth grade, but it is now tenth students less than it was in the fifth grade. How many pupils are in
Harvest time
Grandma and granddaughter Julka reap currants in 15 hours of working together. Julka herself would have currants 10 days after 6 hours of work a day. Find by what percentage the grandma's harvest time was shortened when the granddaughter was involved in c
Before yesterday
He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the
Cut trees
There are 1,200 trees in the grove, of which 55 percent are deciduous, the remaining coniferous. Workers cut down 35 percent a) trees, b) deciduous trees, c) coniferous trees. How many trees now have this grove?
Folding table
The folding kitchen table has a rectangular shape with an area of 168dm² (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu
Prospering students
There are girls and 30 boys in the class. Boys prospering 28, girls all. How many girls are in the class and how many boys are there, if all the prospering students are 95%?
Lemonade
In January, 2 liters of lemonade were sold for CZK 24, while in February, 2.5 liters of lemonade sold at same price. How much percent was 1 liter of lemonade cheaper in February than in January?
Math test
Obelix filled a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points, for each bad answer he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctly?
On a farm
On a farm, there are 90 rabbits, 700 sheep, 300 cattle and 500 pigs. What percentage of the total number of animals are rabbits?
Mushrooms
Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
Discount
The dress was discounted by CZK 115, which was 12% of the original price. What is the cost of the dress after the discount?
Associative law multiplication
In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first)
Utopia Island
The probability of disease A on the island of Utopia is 40%. The probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women o