Question

Six years ago a man's age was six times the age of his son. Four
years hence, thrice his age will be equal to eight times his son's
age. Find their present ages.
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Answer 1

let the present age of man be X and his son be Y.

six years age their age would be X-6 and Y-6.

(X-6)= 6(Y-6). ____________(1)

four years after their age would be

(X+4) and (Y+4)

3(X+4) =8(Y+4) ____________(2)

from 1

X-6= 6Y-36

X=6Y-30

from 2

3X+12= 8Y+32

3X=8Y+20

3(6Y-30)= 8Y+20

18Y-90 = 8Y+20

10Y= 110

Y = 11

X= 6Y-30

X = 6(11)-30

X= 66-30

X= 36

the present age of father is 36 and son is 11.

Answer 2

Answer:

man=36 son=11

Step-by-step explanation:

given,

Six years ago a man's age was six times the age of his son.

small correction in Question the question must be six years ago a man's age was six times the age of his son at that time

let man=m

   son =s

man and son age 6 years ago is

(m-6) and (s-6)

according to Question

(m-6)=6*(s-6)

m-6=6s-36

m-6s=-30   ---------(1)

Four

years hence, thrice his age will be equal to eight times his son's

age at the time

four years hence man's age will be

(m+4) and (s+4)

According to Question,

3(m+4)=8(m+4)

3m+12=8m+32

3m-8m=20-----------(2)

by solving Eq(1) and (2) we get,

m=36 s=11