Re: A class has 4 sections P, Q, R and S, with their average weights of th
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07 May 2024, 11:45
Let the number of students in the sections P, Q, R and S be p, q, r and s, respectively.
Thus, the average weight of all students together in the four sections
\(\frac{Total weight of all the students combined}{Total # of students}\)
\(\frac{45*p+50*q+55*r+65*s}{p+q+r+s}=55\)
Solve
10p+5q=10s
2p+q=2s
Since we need to maximize r , we need to find the minimum possible values of p, q and s so that the above equation holds true.
Since the RHS is 2s, it is even. Also, in the LHS, 2p is even. Thus, q must be even.
Since the smallest even number that we can consider for q is 2, as we have at least one student in each section. Thus, we have q = 2.
Thus, the equation gets modified to:
2p + 2 = 2s
=> p + 1 = s
Thus, we use the minimum possible values: p = 1, s = 2.
Thus, we have p = 1, q = 2 and s = 2.
Since there are a total of 40 students in all sections combined, the maximum value of students in section \(R = r = 40 - (p+q+s) = 40 − 5 = 35\)
The correct answer is Option D