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?

1 Answer
Aug 29, 2016

Jack's IQ is 8080.

Explanation:

Suppose that, Jack's IQ is jj, and those of the rest of the 44

persons in group A, be, x_1,x_2,x_3,x_4x1,x2,x3,x4.

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.!