There were five people in group A, with a mean lQ of 100, and five in group B, with a mean IQ of 74. When Jack left group A for group B, both means increased, and the total of the two new means was 180. What Is Jack's IQ?

Question

Cameron Adams · Accepted Answer

Jack's IQ is #80#.

Suppose that, Jack's IQ is #j#, and those of the rest of the #4# persons in group A, be, #x_1,x_2,x_3,x_4#. Accordingly, #(x_1+x_2+x_3+x_4+j)/5=100...........(1)#. After, leaving the group by Jack, the new mean for the group A is #=(x_1+x_2+x_3+x_4)/4....................(1')#. Let #y_i, 1<=i<=5,# be the IQs of #5# persons of group B. Since, the average IQ of Group be is #74#, we have, #(y_1+y_2+y_3+y_4+y_5)/5=74............(2)# Finally, after Jack's joining the group B, since it has now #6# members, the new mean becomes, #(y_1+y_2+y_3+y_4+y_5+j)/6...................(2')# Using #(1') and (2')# in what is given, we get, #(x_1+x_2+x_3+x_4)/4 + (y_1+y_2+y_3+y_4+y_5+j)/6=180#, or, #3((x_1+x_2+x_3+x_4)+2(y_1+y_2+y_3+y_4+y_5+j)=2160...(3)# Here, #(1) rArr (x_1+x_2+x_3+x_4)=500-j#, and, #(2) rArr (y_1+y_2+y_3+y_4+y_5)=370#. Utilising these in #(3)#, # 3(500-j)+2(370+j)=2160# #:. 1500-3j+740+2j=2160#, i.e., # j=80#. Hence, Jack's IQ is #80#. Enjoy maths.!