Bissoy.com
Doctors Medicines MCQs Q&A

In an examination, the difference of the highest and the least marks is 33. When the average of marks was taken without considering the highest marks then the average was reduced by 2% but when the average of marks was taken without considering the least marks then the average of the marks was increased by 3%. If there are 76 students, find the original average of the marks of all the students?

In an examination, the difference of the highest and the least marks is 33. When the average of marks was taken without considering the highest marks then the average was reduced by 2% but when the average of marks was taken without considering the least marks then the average of the marks was increased by 3%. If there are 76 students, find the original average of the marks of all the students? Correct Answer 8.8

Let the original average of the marks of all the candidates = x

And let the highest and least marks be a and b respectively.

According to the question,

98% of x = (76x – a)/75

98% of 75x + a = 76x      ----(1) 

And 103% of x = (76x – b)/75

103% of 75x + b = 76x    ----(2)

From equations (1) and (2)

98% of 75x + a = 103% of 75x + b

⇒ 5% of 75x = a – b

According to the question,

(a – b) = 33 

∴ 5% of 75x = 33

⇒ 5 × 75x/100 = 33 

By solving, x = 8.8

Related Questions

In a group of 71 people, the difference between the age of the eldest and the youngest person is 35 years. when the average age was taken without considering the eldest person the average was reduced by 3% but when the average was taken without considering the youngest person the average was increased by 2%. Find the original average age of all the people. 
An examination consists of four sections viz. Maths, Science, English and Hindi. Certain number of students registered for the examination in which 12% did not appear for the examination and 8% of the total registered students were not able to clear any section. 12.5% of the appeared students cleared only Maths section, 25% of the appeared students cleared only Maths and Science section. 13% of the total registered students cleared only Maths, Science and English section. If the remaining students who appeared for the examination are 51 and cleared all the four sections, then what is the total number of students who appeared for the examination? (Note: No other case is possible other than given in the question) 
A university library budget committee must reduce exactly five of eight areas of expenditure - I, J, K. L, M, N, O and P - in accordance with the following conditions: If both I and O are reduced, P is also reduced. If L is reduced, neither N nor O is reduced. If M is reduced, J is not reduced. Of the three areas J, K and N exactly two are reduced. If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?
A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions: If both I and O are reduced, P is also reduced.
If L is reduced, neither N nor O is reduced.
If M is reduced, J is not reduced.
Of the three areas J, K, and N exactly two are reduced. Question : If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?
The average marks obtained by 140 students in an examination is 90. If the average marks of students who passed the examination are 120 and the number of students who failed the examination is 90, then what are the average marks of the students who failed the examination?
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 choose the correct option. Quantity A: Vinay secured 92.5% marks in an examination comprising of 5 subjects each of 120 marks. He scored 95% marks in English and Hindi together, while 90% marks in Mathematics. In Science, if he scored one marks more than Social studies, how many marks did he scored in Science? Quantity B: Ashi scored 75%, 80% and 90% marks in Physics, Chemistry and Mathematics sections respectively, in an examination of total 150 marks. If the Physics and Chemistry sections are worth 40% and 20% of the total marks, how many marks did Ashi secured in the examination? 
The conditions regarding selection from a list of suitable candidates to be called for interview after a written examination for appointment of management-level persons to a multi-national company providing accounting services and sales are mentioned below. Candidates: a) Must have a Bachelor's degree in Basic Science with 65% or more marks or BE with 55% or more marks. b) Must have passed the examination with 70% or more marks. c) Age must be between 25 to 30 years as of 1/4/18. d) Must have 3 years of experience in an Accounting Institution and must have a Diploma in Accounting with 60% or more marks. e) Must be currently getting CTC of Rs. 6 lakh or more per annum. If the candidate: 1) If he fulfills all the other conditions other than A above, he will be designated as Junior Accountant. 2) If he fulfills all the other conditions other than (d) and (e) above, he can be designated as Trainee-Accountant. If he fulfills all the above conditions including 5 years of experience, he can be designated as a Senior Accountant. He can be designated as Manager (Accounts) if he fulfills all the above criteria including educational qualifications of CA/ ICWA/ MBA (Finance). Study all the above information and answer the following question. Varun has passed the CA exam and has a bachelor's degree in basic science and a diploma in accountancy, having scored 75% or more in the written examination during his entire career and also in the written examination. His age is 27 years and with 4 years of experience in Accountancy, he has a CTC salary of 18 lakhs per annum. To which of the following positions can he be referred? Select from the given options.
Several students have taken an exam. There was an error in the answer key which affected the marks of 48 students, and their average marks reduced from 78 to 66. The average of remaining students increased by 3.5 marks. This resulted the reduction of the average of all students by 4.5 marks. The number of students that attended the exam is:
Study the following information carefully to answer the questions given below. AGS organization is conducting an interview. Following are the criteria for a certain post. All these cases are given as of 1.05.2017. The candidate must: A. Be an engineering graduate with at least 70% marks. B. Be not less than 21 years and not more than 30 years of age as of 1.05.2017. C. Have passed the selection test with at least 60% marks. D. Be willing to pay a deposit of 60,000/-, to be refunded on completion of training. However, if the candidate fulfills the above-mentioned criteria except: I. At (A) above, but has appeared for the last semester examination, and has obtained an aggregate of 75% marks in first 7 semesters, his/her case may be referred to the V.P of the company. II. At (D) above, but is willing to pay an amount of at least Rs. 30,000/- and has obtained at least 80% marks at engineering degree, his/her case may be referred to the general manager of the company. Ranjith has appeared for the last semester of the engineering degree exam and expects to score as least 76% marks. His aggregate score up to the first 7 semesters is 82%. He has just completed 21 years of age as of 1.05.2017. He has scored 63% in the selection test and is ready to pay an amount of 60,000/- as a deposit.
In an examination, there were three subjects Hindi, Maths, and Science. Marks scored by Karan in Hindi is 60. Marks scored by Karan and Lokesh in Maths is equal. Marks scored in 3 subjects by Lokesh is 200. Marks scored by Lokesh in science is 25 % of total marks obtained. Marks scored by Mohit in Hindi is equal to marks scored by Lokesh in Maths. Marks scored in Maths by Mohit is 5 more than the marks scored in Hindi. Marks scored in Maths by Lokesh is 20 more than marks scored in Science. Marks obtained by Karan, Lokesh, and Mohit in Hindi are what percent of marks obtained by Karan, Lokesh, and Mohit in Maths?