Two children weighing 17 and 20 kilograms are sitting on opposite sides of a seesaw, both 2 meters from the axis of rotation. where on the seesaw should a 10-kilogram child sit in order to achieve equilibrium?

In order to achieve an equilibrium some of momentum should be zero about the axis of rotation.

Suppose, the 10-kilogram child is placed X meters away from the axis of rotation.

Now, according to the question

17x2+10X-20x2=0

X=0.6m

Child should sit 0.6m away from the axis of rotation towards 17 Kg child.