CAT: Averages & Mixture Test

The average score of 25 students in a test is 50. The five highest-scoring students obtain the same score. The scores of the remaining students are distinct integers, with the lowest score being 30. What is the maximum possible score obtained by each of the five highest-scoring students?

A certain quantity of an alloy containing silver and copper is mixed with 3 kg of pure silver, resulting in a mixture containing 90% silver by weight. The same quantity of the original alloy is instead mixed with 2 kg of another alloy containing 90% silver, producing a mixture containing 84% silver by weight. The weight of the original alloy, in kg, is:

A basketball player has already played a certain number of games, with 10 more games remaining in the season. If he scores a total of 1 point in the next 10 games, his overall average will be 0.15 points per game. However, if he scores 2 points in those 10 games, his overall average will be 0.2 points per game. The number of games he has already played is:

A chemical solution has its concentration expressed as the amount of chemical, in grams, present in every 100 ml of solution. Two 800 ml containers hold solutions with concentrations of 33% and 17%, respectively. Some quantity of the solution from the first container is removed and replaced with the same quantity taken from the second container. If the concentration in the first container becomes 21%, then the quantity of solution remaining in the second container, in ml, is:

A bakery sells a particular type of pastry every day. The average number of pastries sold per day during the first seven days is 60, while the average for the first eight days is 63. On the ninth day, the bakery sells 11 fewer pastries than it sold on the eighth day. As a result, the average number of pastries sold per day from the second day to the ninth day becomes 66. How many pastries were sold on the first day?

Consider all 4-digit even natural numbers of the form "aabb", where a > 0. Here, the first two digits are identical, as are the last two digits. What is the arithmetic mean of all such numbers?