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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=$m*n$

total weight of the class=1600+mn

new average of the class=$1600+mn/40+m$

we can write it as a function of m

f(m)=$1600+m(50-m)/40+m$ where n+m=50

f(m)=$1600+m(50-m)/40+m$

for finding the maximum value , we will differentiate this function

f'(m)=$(40+m)(50-2m)-1600+m(50-m)/(40+m)^2$

f'(m)=0 for maximum value

by solving we get

$(40+m)(50-2m)-1600+m(50-m)/(40+m)^2$

$m=4.72,&space;n=45.27$

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

$f(m)=1600+4.75(50-4.72)/40+45.27&space;=&space;40.56$

(B) is the correct option