Six years hence a man’s age will be three times his son’s age, and three years ago he was nine times as old as his son at that time. Find their present ages.
Answers
Answer:
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)y+6=3(x+6) andy−3=9(x−3)
\begin{gathered}\begin{array}{l}{y+6=3 x+18} \\ {3 x-y+18-6=0}\end{array}\end{gathered}
y+6=3x+18
3x−y+18−6=0
3 x-y+12=0--------(1)3x−y+12=0−−−−−−−−(1)
Also, y-3=9 x-27y−3=9x−27
\begin{gathered}\begin{array}{l}{9 x-y-27+3=0} \\ {9 x-y-24=0}\end{array}\end{gathered}
9x−y−27+3=0
9x−y−24=0
(1)– (2) gives 3 x-y+12-9 x+y+24=03x−y+12−9x+y+24=0
\begin{gathered}\begin{array}{l}{-6 x+36=0} \\ {6 x-36=0} \\ {6 x=36} \\ {x=6}\end{array}\end{gathered}
−6x+36=0
6x−36=0
6x=36
x=6
from (1) y=3 x+12=3(6)+12=18+12=30y=3x+12=3(6)+12=18+12=30
Therefore,the man’s present age is 30 and the son’s present age is 6.
Answer:
Let the age of man be x
and the age of his son be y
According to the question:
After 6 years :
(x+6)=3(y+6)
⇒x−3y=12⟶(i)
Three years ago :
x−3=9(y−3)
⇒x−3=9y−27
⇒x−9y=−24⟶(ii)
Solving (i) and (ii),
6y=36
⇒y=6
Putting value of y in equation (i),
x−3xy=12
∴x=12+18
x=30
∴ Age of man =30 years.
Age of son =6 years.