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Question

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

CAT 2021

A
40.18 kgs
CORRECT ANSWER WRONG ANSWER
B
40.56 kgs
CORRECT ANSWERWRONG ANSWER
C
40.67 kgs
CORRECT ANSWER WRONG ANSWER
D
40.49 kgs
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(B)

Explanatory Answer

Total weight of 40 students = 40*40=1600

m students join with n average weight

n additional weight=

total weight of the class=1600+mn

new average of the class=

we can write it as a function of m

f(m)= where n+m=50

f(m)=

for finding the maximum value , we will differentiate this function

f'(m)=

f'(m)=0 for maximum value

by solving we get

by putting these values in f(m) , we get

(B) is the correct option