Average Age Puzzle

An average is the sum of the values of a sample set divided by the number samples in the set.

The first set has an average of 30 with 10 samples. This means the sum of all of the ages of the people in the room is 300.

The second set has an average of 27 with 8 samples. This makes the Sum of the remaining 8 individuals 216.

The Sum of the ages of the 2 who left the room then must be 84. Divide that by 2 for the average of their age and you end with an answer of 42.

It's the only answer more than 30...

there are ten people.

Let 8 people be in a group that we call X. And 2 people in the group Y.

The total average is

                                     (X+Y) / 10 = 30

                                     X+Y = 300       (i)

now when the two persons go out, average of 8 persons becomes 27, so

                                    X / 8 = 27

                                     X = 216

Put value of X in (i) we get

                                   216 + Y = 300

                                    Y = 84

where Y is their combined age so the average is

average of Y = Y / 2 = 84 / 2 = 42.

This can also be done using simultaneous equations.So,let X be the total age of the common 8 people and Y be the total age of the other two people. We have, X/8=27-------1 and (X+Y)/10=30-------2. If we solve equation 1,then we have X=216.So substitute that into equation 2 and we have (216+Y)/10=30, Y=300-216, Y=84. As Y was the total age of the two people that left,therefore average age of the two people is Y/2 = 84/2 = 42.

If you have that the average age goes down by 3, the average for each person goes down by 3. If the average for each goes down by 3, the total would go down by 3*10 which is 30. Then since 2 people left, they would each make the average go down by 15. So if you add 15 from the 27 to get an average of 42 for the two people who left.