Quant Exam > Quant Questions > Consider a class of 40 students whose average...
Start Learning for Free
Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?
- a)40.18 Kgs
- b)40.56 Kgs
- c)40.67 Kgs
- d)40.49 Kgs
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider a class of 40 students whose average weight is 40 kgs. m new ...
Solution:
Given, the class has 40 students with an average weight of 40 kgs.
Let the total weight of these 40 students be W1.
W1 = 40 x 40 = 1600 kgs
Now, m new students join the class with an average weight of n kgs.
Let the total weight of these m students be W2.
W2 = m x n
Also, m x n = 50
So, n = 50/m
Total number of students in the class now = 40 + m
Let the new average weight of the class be x kgs.
Then, we can write:
x = (W1 + W2)/(40 + m)
Substituting the values of W1 and W2, we get:
x = (1600 + mn)/(40 + m)
Substituting n = 50/m, we get:
x = (1600 + 50)/(40 + m)
x = (1650)/(40 + m)
To find the maximum value of x, we need to differentiate it with respect to m and equate it to zero.
dx/dm = -1650/(40 + m)^2 = 0
40 + m = sqrt(1650)
m = sqrt(1650) - 40
Substituting this value of m in the equation for x, we get:
x = 40 + (50/sqrt(1650) - 1)
x = 40.56 kgs (approx)
Therefore, the maximum possible average weight of the class now is 40.56 kgs (option B).
Given, the class has 40 students with an average weight of 40 kgs.
Let the total weight of these 40 students be W1.
W1 = 40 x 40 = 1600 kgs
Now, m new students join the class with an average weight of n kgs.
Let the total weight of these m students be W2.
W2 = m x n
Also, m x n = 50
So, n = 50/m
Total number of students in the class now = 40 + m
Let the new average weight of the class be x kgs.
Then, we can write:
x = (W1 + W2)/(40 + m)
Substituting the values of W1 and W2, we get:
x = (1600 + mn)/(40 + m)
Substituting n = 50/m, we get:
x = (1600 + 50)/(40 + m)
x = (1650)/(40 + m)
To find the maximum value of x, we need to differentiate it with respect to m and equate it to zero.
dx/dm = -1650/(40 + m)^2 = 0
40 + m = sqrt(1650)
m = sqrt(1650) - 40
Substituting this value of m in the equation for x, we get:
x = 40 + (50/sqrt(1650) - 1)
x = 40.56 kgs (approx)
Therefore, the maximum possible average weight of the class now is 40.56 kgs (option B).
Free Test
FREE
| Start Free Test |
Community Answer
Consider a class of 40 students whose average weight is 40 kgs. m new ...
If the overall average weight has to increase after the new people are added, the average weight of the new entrants has to be higher than 40.
So, n > 40
Consequently, m has to be < 10 (as n + m = 50)
Working with the “differences"? approach, we know that the total additional weight added by “m"? students would be (n - 40) each, above the already existing average of 40. m(n - 40) is the total extra additional weight added, which is shared amongst 40 + m students.
So, m * (n−40)(m+40)(n−40)(m+40) has to be maximum for the overall average to be maximum.
At this point, use the trial and error approach (or else, go with the answer options) to arrive at the answer.
So, n > 40
Consequently, m has to be < 10 (as n + m = 50)
Working with the “differences"? approach, we know that the total additional weight added by “m"? students would be (n - 40) each, above the already existing average of 40. m(n - 40) is the total extra additional weight added, which is shared amongst 40 + m students.
So, m * (n−40)(m+40)(n−40)(m+40) has to be maximum for the overall average to be maximum.
At this point, use the trial and error approach (or else, go with the answer options) to arrive at the answer.
The maximum average occurs when m = 5, and n = 45
And the average is 40 + (45 – 40) * 545545 = 40 + 5959 = 40.56 kgs
And the average is 40 + (45 – 40) * 545545 = 40 + 5959 = 40.56 kgs
The question is "what is the maximum possible average weight of the class now?"
Hence, the answer is "40.56 kgs".
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer?
Question Description
Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer?.
Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?a)40.18 Kgsb)40.56 Kgsc)40.67 Kgsd)40.49 KgsCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup