This is the basic and exam oriented question from linear equations in two variables in which we have to find the age of father and son if 2 years ago, a father was five times as old as his son. 2 years later, his age will be 8 more than three times the age of the son.

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 43

## Let father age beÂ x, his son age beÂ y.

BeforeÂ 2Â years,

â‡’(xâˆ’2)=5(yâˆ’2)âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’(1)

After 2 years

â‡’(x+2)=8+3(y+2)âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’(2)

From (1)Â xâˆ’5y+8=0

From (2)

â‡’x+2âˆ’3yâˆ’6âˆ’8=0

â‡’xâˆ’3yâˆ’12=0

Solving them

â‡’âˆ’2y+20=0

â‡’y=10

WhenÂ y=10,x=42

So the present age of the father isÂ 42Â and the son age isÂ 10.