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?
Answers
Answer:
Max possible Average Weight = 40.5555 kg
Step-by-step explanation:
a class of 40 students whose average weight is 40 kgs.
Total Weight = Average Weight * Number of Students
=> Total Weight = 40 * 40
=> Total Weight = 1600 kg
M New Students Joins
Average Weight of M Students = N kg
Total Weight of M Students = MN kg
New Total Weight = 1600 + MN
Total Students = 40 + M
New Average Weight = (1600 + MN)/(40 + M)
M + N = 50
=> N = 50 - M
=> New Average Weight = (1600 + M(50 - M))/(40 + M)
=> (-M² + 50M + 1600)/(M + 40)
Differentiating wrt M
=> (-2M + 50)/(M + 40) - (-M² + 50M + 1600)/(M + 40)²
Equating to Zero
=> (-2M + 50)/(M + 40) - (-M² + 50M + 1600)/(M + 40)² = 0
=> (M + 40)(-2M + 50) +M² - 50M - 1600 = 0
=> -2M² -30M + 2000 + M² - 50M - 1600
=> -M² -80M + 400 = 0
=> M² +80M - 400 = 0
=> M = 4.72
as M has to be Integer
So lets see for M = 5 & M = 4
(1600 + MN)/(40 + M)
for M = 5 . N = 45
= (1600 + 5*45)/(40 + 5)
= 40.5555 kg
for M = 4 . N = 46
= (1600 + 4*46)/(40 + 4)
= 40.5454 kg
40.5555 > 40.5454
Max possible Average Weight = 40.5555 kg