2 celestial bodies are separated by some distance.if the mass of any 1 of the point like bodies s doubled while the mass of the other is halved then how far should they be taken so that the gravitational force between them becomes one fourth

Dear student

Let initially two body have same masses say m and separated by a distance d then the gravitational force b/w them 
$F=\frac{G{m}^2}{d^2}$       ............(1)

Now the mass of one body becomes half and double for the other and let the distance b/w them is r so that the force becomes F/4 hence 
$$\begin{gathered} \frac{F}{4}=\frac{G·2m·{\displaystyle \frac{m}{2}}}{r^2} \\ u\sin g eq. \left(1\right) \\ \frac{1}{4}\frac{G{m}^2}{d^2}=\frac{G{m}^2}{r^2} \\ {r}^2=4d^2 \\ r=2d \\ so dis\tan ce b/w the bodies will be doubled. \end{gathered}$$