Question

6 years hence a man's age will be 3 times his son's age and three years ago he was nine times as old as his son. find their present ages?

Answer 1

hope this may helps you:-)

Answer 2

son’s age is 6 and father’s age is 30.  

Given:  

3 years ago,a man’s age was 9 times as old as his son.  

Also,man’s age will be 3 times his son’s age 6 years later.  

To find:  

Present age of son and father  =?

Solution:

Let the son’s present age be ‘x’,man’s age be ‘y’  

Then,  $y+6=3(x+6)  and y-3=9(x-3)$

$\begin{array}{l}{y+6=3 x+18} \\ {3 x-y+18-6=0}\end{array}$

$3 x-y+12=0--------(1)$

Also, $y-3=9 x-27$

$\begin{array}{l}{9 x-y-27+3=0} \\ {9 x-y-24=0}\end{array}$

(1)– (2) gives $3 x-y+12-9 x+y+24=0$

$\begin{array}{l}{-6 x+36=0} \\ {6 x-36=0} \\ {6 x=36} \\ {x=6}\end{array}$

from (1) $y=3 x+12=3(6)+12=18+12=30$

Therefore,the man’s present age is 30 and the son’s present age is 6.