Two forces acting on a particle in opposite directions have a resultant of 10 kg wt. If they act at right angles to each other, the resultant is 60kg wt. The forces are (in kg. wt):

The correct option is A 47.4, 37.4
When forces are in opposite direction the net magnitude is $10$.
Let the forces be $x$ and $10+x$.
When they act in $90$ degrees, the net magnitude is $60$
Therefore,
$60=\sqrt{x^2+(10+x{)}^2}$
$3600=2x^2+100+20x$

$2x^2+20x-3500=0$

$x^2+10x-1750=0$
Solving the quadratic equation gives $x=37.4$ or $x=-47.4$ but since magnitude is always positive $x=37.4$ and the other force is $47.4$.