Question

The sum of three times the age of son and the age of his father is 110. If three times the age of his is added to the age of son we get 170

1)What is the sum of their age

2)Find their ages

Answer 1

Let the age of son be x and father be y

So according to first condition,
3x + y = 110 .........(1)

and according to second condition,
3y + x = 170..........(2)

Now adding (2) and (1)

=> 3x + y + 3y + x = 170 + 110

=> 4x + 4y = 280

=> 4(x + y) = 280

=> x + y = 280/4

=> x + y = 70.............(3)

So your first answer, the sum of their ages is 70

Now Subtracting (1) from (2)

=> 3y + x - (3x + y) = 170 - 110

=> 3y + x - 3x - y = 60

=> 2y - 2x = 60

=> 2(y - x) = 60

=> y - x = 60/2

=> y - x = 30...........(4)

Adding (3) and (4)

=> x + y + y - x = 70 + 30

=> 2y = 100

=> y = 100/2

=] y = 50

Now putting the value of y in (3)

x + y = 70

=> x + 50 = 70

=> x = 70 - 50

=> x = 20

So the age of father is 50 years and the age of son is 20 years


Hope it helps dear friend ☺️✌️