Question

4 years ago a father was 6 times as old as his son and 10 years later the father will be 2 and half times as old as his son determine the present age of father and his son

Answer 1

let the present age of father be x yrs and his son be y yrs
4 years ago,
father's age=(x-4)yrs
son's age=(y-4)yrs
10 yrs later
father's age=(x+10)yrs
son's age=(y+10)yrs
A/Q
x-4=6(y-4)
x-4=6y-24
x-6y=-20. (1)×2
And,
x+10=5/2(y+10)
x+10=5/2y+25
×-5/2y=25-10
2x-5y/2=15
2x-5y=30. (2)×1
multiplying (1) by2 and (2) by 1,
2x-12y= -40
2x-5y= 30
(-) (+) (-)
___________
-7y= -70
y = -70/ -7
y = 10
putting y=10 in equation (1)
x - 6×10 = -20
x = -20+60
x = 40
Hence,
father's present age=40 yrs
son's present age = 10yrs
hopes it helps

Answer 2

Answer:

let the present age of father be x yrs and his son be y yrs

4 years ago,

father's age=(x-4)yrs

son's age=(y-4)yrs

10 yrs later

father's age=(x+10)yrs

son's age=(y+10)yrs

A/Q

x-4=6(y-4)

x-4=6y-24

x-6y=-20. (1)×2

And,

x+10=5/2(y+10)

x+10=5/2y+25

×-5/2y=25-10

2x-5y/2=15

2x-5y=30. (2)×1

multiplying (1) by2 and (2) by 1,

2x-12y= -40

2x-5y= 30

(-) (+) (-)

___________

-7y= -70

y = -70/ -7

y = 10

putting y=10 in equation (1)

x - 6×10 = -20

x = -20+60

x = 40

Hence,

father's present age=40 yrs

son's present age = 10yrs

hopes it helps