very difficult question !!!!!

Let M be the test mass
Force acting on test mass by mass P = GMm/x^2
Force acting on the test mass by mass Q = GM(4m)/(4r - x)^2
where G is the Universal Graviatational Constant

It is given that the net force acting on the test mass is zero
Hence, GMm/x^2 = GM(4m)/(4r - x)^2
i.e. (4r - x)^2 = 4x^2
Taking square-root on both sides
4r - x = 2x or 4r - x = -2x
x = 4r/3 or -4r (rejected, as the resultant gravitational force is not zero under this situation)
Therefore x = 4r/3