ratio and propotion

Question

The average age of a board of 8 functional directors in a company is the same as it was 3 years ago , a younger man having been substituted for one of the directors . How much younger was the new man than the director whose place he took.

 

(a)12

(b)15

(c)18

(d)21

(e)24

Answer 1

Let y = age of the younger man now

     d = age now of the director that was replaced

     S = sum of ages of the other 7 directors now

 

Three years ago, the age of the younger man was y-3, the age of the replaced director was d-3, and the sum of the ages of the other 7 directors was S-21.

 

Average age now = (sum of ages of the 8 directors now)/8

 

                         = (y + S)/8

 

Average age 3 years ago = (d - 3 + S - 21)/8

 

So, (y + S)/8 = (d - 3 + S - 21)/8

 

Therefore, y + S = d + S - 24

 

                    y = d - 24

 

The age of the younger man now is 24 years less than the replaced director's age now.