Bissoy.com
Doctors Medicines MCQs Q&A

The average weight of some students in a group is 42 kg. If 8 students having average weight 44 kg leave the group and 3 students having average weight 48.25 kg join the group, the average weight of the new group is 50 g more than that of the original group. How many students were there in the group initially?

The average weight of some students in a group is 42 kg. If 8 students having average weight 44 kg leave the group and 3 students having average weight 48.25 kg join the group, the average weight of the new group is 50 g more than that of the original group. How many students were there in the group initially? Correct Answer 60

Given:

Average weight of some students = 42 kg

Average weight of 8 students who leave = 44 kg

Average weight of 3 students who join = 48.25 kg

Concept used:

Average = Sum of elements/No. of elements

Calculation:

Let total number of students in the group be x

Average weight of x students = 42 

Sum of weight of x students = 42x

Average weight of 8 students = 44 

Sum of weight of 8 students = 44 × 8 = 352

Average weight of 3 students = 48.25

Sum of weight of 4 students = 48.25 × 3 = 144.75

According to the question,

42x – 352 + 144.75 = (x – 8 + 3) × (42 + 0.05)

⇒ 42x – 207.25 = (x – 5) × 42.05 

⇒ 42x – 207.25 = 42.05x – 210.25 

⇒ 42.05x – 42x = 210.25 – 207.25

⇒ 0.05x = 3

⇒ x = 5/0.05 

⇒ x = 60 

∴ Initially 60 students were in the group.

Related Questions

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the average weight of new students added? I. In a class 60% students are male and there average weight is 15 kg more than the female students, 9 males and 6 new female students joined the class and the average weight of the class increased by 0.84 II. Total male students in the class is 12 more than female students adding 9 male students to the class increases the average weight of male students by 1 kg and adding 6 female students increases the average weight of female students by 0.6.
Questions below followed by three quantities. Find the relationship between them. Quantity I: In a class with a certain number of students if a teacher weighing 78 kg is added, then average weight of class is increased by 2 kg. If one more teacher weighing 66 kg is added, then the average weight of the class increases by 3.5 kg over the original average. What is the original average weight (in kg) of the class? Quantity II: The average age of 16 students and their teacher's age is 16 years. If the teacher's age is excluded, the average reduces by 2. What is the teacher's age? Quantity III: Average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average is 45 kg. If another person E whose weight is 6 kg more than D, joins the group replacing A, then average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)?
There are six persons namely A, B, C, D, E and F. They all take leave from office on any one day of the week starting from Monday to Saturday. Only one person takes leave on one day. C is the first person to take a leave. Three persons take leave between D and C. F takes leave just after D. E takes leave on Wednesday. B takes a leave after A. Who takes a leave on Thursday?
The average weight of some persons in a group is 76 kg. If 15 persons with average weight 72 kg join the group or 5 persons with average weight 84 kg leave the group, the average weight of the persons in the group in both cases is the same. How many persons were there in the group, initially?
The average weight of some persons in a group is 72 kg. When 5 persons with average weight 66.6 kg join and 13 persons with average weight 75 kg leave the group, the average weight of the persons in the group decreases by 1.65 kg. How many persons were there in the group initially?
The average weight of some boys in a group is 45 kg. If 10 boys with an average weight of 39 kg join the group or 10 boys with an average weight of 49 kg leave the group, then the average weight of boys in both cases is equal. How many boys were there in the group initially?
The average height of a certain number of students in a group is 155.6 cm. If 12 students having an average height of 150.5 cm join the group and 7 students having an average height of 159 cm leave the group, the average height of the students in the group will decrease by 34 mm. What is the number of students, initially, in the group?
If 10 employees in an organization having an average weight of 73 kg leave and 5 employees having an average weight of 70 kg join, the average weight of the employees in the organization decreases by 0.4 kg. The average weight of all employees in the organization initially is 70 kg. If the number of employees initially in the organization is n, which of the following is/are correct? I. 73 employees are left II. n is a multiple of 16 III. 70 < n < 80
In a survey of 900 students, 400 students were interviewed in TCS, 310 students were interviewed in IBM and 470 students were interviewed in Infosys. Also, 110 students were interviewed in both TCS and IBM, 80 students were interviewed in both IBM and Infosys and 140 students were interviewed in both TCS and Infosys. If 50 students were interviewed in all three companies. Then, how many students were interviewed in only TCS?
The average weight of some members of a club is 70 kg. If 15 members with an average weight of 60 kg join the club or 5 members with an average weight of 90 kg leave the club, then the average weight of members in both cases is equal. How many members were there in the club initially?