Question

Five years ago, father was thrice as old as his son 10 years later, Father's age will be
twice the age of his son then.
Represent the above statements by two linear equations in two variables.​

Answer 1

Answer:

Let the present age of father be x and the present age of his son be y

5 years ago, father's age was thrice than his son

X - 5 = 3(y-5)

x - 5 = 3y - 15

X - 5 - 3y +15 =0

X - 3y = - 10..... (1)

10 years later the age of his father will be twice than his son

(X + 10) = 2(y +10)

X +10 = 2y +20

X - 2y +10 - 20 = 0

X - 2y = 10......... (2)

Solving (1) and (2) by elimination

X - 3y = - 10

X - 2y = 10

- + -

-------------------------

- Y = - 20

Y =20 yrs

From eq. (2) x - 2y =10

X - 2(20) =10

X =10 +40

X =50 years

So, the present age of father is 50 yrs and that of his son is 20 years

Let's verify

Put the value of x as 50 and y as 20

In the equation

X-3y =-10 eq (1)

50 - 3(20) = - 10

50 - 60 = - 10

-10 = - 10

L.H.S = R. H. S

Hence, verified