Averages

Radha distributes 5 sweets to each of her friends, Arjun, Deepika, Govind, and Jaya. The following three points are valid for the sweets with Arjun, Deepika, Govind, and Jaya before they receive the sweets from Radha. (i) The number of sweets with Arjun was equal to one-third of that with Govind. (ii) The average number of sweets with Jaya and Deepika was 27. (iii) The average number of sweets with Govind, Jaya, and Deepika was 30. What must be the average number of sweets with Govind, Arjun, Deepika, and Jaya now?

Sikha was reading a book when she received a phone call from her friend. While she was attending the call, her pet cat Garfield tore a leaf from the book. [A leaf consists of two pages numbered with consecutive numbers]. If the average of all the page numbers that remained was 40⁵/₁₁, then the sum of the page numbers on the leaf that was torn by Garfield was

Consider a sequence of 40 integers, denoted as a1, a2, ..., a40, where a1 is smaller than a2, a2 is smaller than a3, and so on in the increasing order. If the average of these 40 integers is three less than the average of the remaining integers a2, a3, ..., a40, and it is given that a40 equals 120, what is the maximum value that a1 can attain?

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40,000, of the last 30 employees was Rs. 60,000, and of the first 10 and last 10 employees together was Rs. 50,000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

In a quiz contest, there are 5 girls and 7 boys, and their average score is 30. Every girl scores the same number of points, and every boy scores the same number of points. If each girl's score is no less than a boy's score and at most three times a boy's score, how many distinct integer values are possible for the total score of 5 girls together with 9 boys?

At Greenwood High School, 50 students took two unit assessments in Mathematics, each scored out of 50 marks. In Assessment 1, the average score of the first 30 students (arranged by ascending ID numbers) was 30, while the average score of the last 30 students was 42. The combined average score of the first 20 and the last 20 students was 36. In Assessment 2, each student's score was calculated relative to their Assessment 1 score: the first 20 students' scores increased by 30%, the next 10 students' scores remained unchanged, and the last 20 students' scores decreased by 30% What was the average score per student (out of 50) in Assessment 2?