Two children weighing 17 and 25 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?

The principle of moments states that for a system at equilibrium the clockwise moments is equal to the anticlockwise moments.

Moments is given by force * perpendicular distance

Moments one one side of the seesaw will be 340Nm and on the other will be 500Nm, for balanced or equilibrium to be achieved the two moments should be equal.

Difference is 160 Nm, thus with a child 10 kg to balance the system, then,

Distance will be 16 nm / 100N = 1.6 m

Threfore, a child of 10 kg should sit at a distance of 1.6m from the pivot on the side with 17 kg child for the system to balance.