A

Step 1: Understanding the Problem
We have two forces, P and Q, acting on a point. If one of the forces is reversed, the resultant of these forces turns through a right angle.

Step 2: Resolving Forces
Assume P acts in the positive x-direction (to the right) and Q acts in the positive y-direction (up). The vector representation of these forces can be written as:
$$ extbf{P} = P extbf{i} $$
$$ extbf{Q} = Q extbf{j} $$

Step 3: Finding the Resultant
The resultant vector, R, of the two forces is:
$$ extbf{R} = extbf{P} + extbf{Q} = P extbf{i} + Q extbf{j} $$

When we reverse the direction of Q, we have:
$$ extbf{R}' = P extbf{i} - Q extbf{j} $$

Step 4: Condition for Right Angles
For R and R' to be perpendicular, the dot product must be zero:
$$ extbf{R} ullet extbf{R}' = 0 $$
Calculating the dot product:
$$ (P extbf{i} + Q extbf{j}) ullet (P extbf{i} - Q extbf{j}) = P^2 - Q^2 = 0 $$

Setting this equal to zero gives:
$$ P^2 = Q^2 $$

Step 5: Conclusion
Taking the positive square root of both sides results in:
$$ P = Q $$

Thus, we have shown that for the resultant to turn through a right angle when one force is reversed, P must equal Q. Therefore, the answer is A.