The greatest and least resultant of two forces acting at a point is 10 N and 6 N respectively.

Let F1 and F2 be the two forces.

Greatest resultant of these two forces is F1+F2=10 N

Least resultant of these two forces is F1-F2=6 N

On solving above two equation,

F1=8 N and F2=2 N

When each force is increased by 3N, then new force will become,

· F'1=F1+3 N=8+3=11 N

· F'2=F2+3 N=2+3=5 N

Since new forces are acting at a point at an angle of 90^o with each other, then resultant force is

R = F'12+F'22 = 112+52 = 146 =12.08 N