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

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWERWRONG ANSWER

CORRECT ANSWER WRONG ANSWER

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

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

$m=4.72, n=45.27$

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

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

(B) is the correct option