Bissoy.com
Doctors Medicines MCQs Q&A

A class teacher calculates the average height of the class of 13 students as 152 cm. Due to the transfer of the parents, 2 students of heights 161 cm and 133 cm leave the school and are replaced by 2 new students whose heights are in the ratio 2 : 3. After this change, the average height of the class increases by 2. Find the heights of the new students.

A class teacher calculates the average height of the class of 13 students as 152 cm. Due to the transfer of the parents, 2 students of heights 161 cm and 133 cm leave the school and are replaced by 2 new students whose heights are in the ratio 2 : 3. After this change, the average height of the class increases by 2. Find the heights of the new students. Correct Answer 128 cm, 192 cm

Given:

Average height of class initially = 152 cm

Average height of class when 2 new students join = 154 cm

Number of students in class = 13

Heights of students who left the school = (161 cm, 133 cm)

Ratio of heights of new students = 2 : 3

Formula Used:

Average Height = Sum of heights/Total number of students

Calculations:

Let the total sum of heights of students be s.

Let the sum of heights of students who are in the school permanently be s’.

Let the heights of new students be h and H respectively.

Sum of heights of all the students = s = 152 × 13

⇒ s = 1976 cm

Sum of heights of students who left the school = (161 + 133) cm

⇒ Sum of heights of students who left the school = 294 cm

When 2 old students left the school,

s = s’ + 294

⇒ 1976 cm = s’ + 294 cm

⇒ s’ = 1682 cm

When 2 new students join the school,

Average height = 154 cm

⇒ Sum of heights of all the students = 154 × 13 = 2002 cm

2002 cm = s’ + (h + H)

⇒ 2002 cm = 1682 cm + (h + H)

⇒ (h + H) = 320

h : H = 2 : 3

1 unit = 320/(2 + 3) = 64

⇒ h = 2 × 64 cm = 128 cm

⇒ H = 3 × 64 cm = 192 cm

∴ The heights of the new students are 128 cm and 192 cm respectively.

Related Questions

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?
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.
Principle: Even if a person suffers a loss, he will be entitled to receive compensation only if a legal right is violated.
Factual Situation: An English teacher in a famous 'English School' after having some rift with the management left the school and started a new 'Language School' very close to the English School. Many students of the English School left it and joined the new Language School. As a result, the English School suffered huge financial loss and hence filed a suit for compensation against the new school.
The average of the height of the 20 employee of the company is 1.5 m.In the month of June, two employees named Rita and Sumit left the company whose height are 1.4 m and 1.6 m respectively. In August, two more people left the company whose average of height is 1.7 m and one person join the company whose height is 87.5% of height of Sumit. Before the December, more four people left the company whose height are 1.3 m, 1.1 m, 1.32 m and 1.25 m respectively and more 5 people join the company whose height are 1.26 m, 1.18 m, 1.39 m and 1.4 m respectively. The average of height in the month of September is ….
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
In an Exam; The % of students qualified to the no.of students appeared from school 'A' is 80%. In school 'B'. The no of students appeared is 25% more than the students appeared from school A and no of students qualified from school 'B' is 40% more than the Students qualified from School 'A'. what is the % of students qualified to the no. of students appeared form school B?
In an examination, the percentage of students qualified to the number of students appeared from school A is 70%. In school B, the number of students appeared is 20% more than the students appeared from school A and the number of students qualified from school B is 50% more than the students qualified from school A. What is the percentage of students qualified to the number of students appeared from school B ?
Eight teachers of different departments - English, math, accounts, economics, geography, biology, chemistry and sociology went for a meeting. There are 2 rows. Each row contains 4 teachers. Teachers of biology and chemistry are sitting adjacent to each other. Opposite to chemistry teacher is accounts teacher who is at extreme left end of south face row. Teacher of English department is sitting somewhere in north facing row but not at any extreme end. Math teacher is sitting second to the right of accounts teacher. Economics teacher is not sitting opposite to biology teacher and not adjacent to English teacher. Where is economics department teacher sitting?
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: The average weight of 24 men is increased by 1.5 kg when a man in the crew whose weight is 50 kg is replaced by a new man. Find the weight of the new man? Quantity B: The average weight of a class of 40 students is 46 kg. If the weight of teacher is included with the students, the new average becomes 47 kg. Find the weight of teacher?