Question

If the distance between two bodies is increased 4times by what factor should the mass of the bodies be altered so that the gravitational force between them remains the same

Answer 1

we know that F=GMm/R²
f=GMm/(4R)²                     (f and F are different)
If f=F, 
GMm/R²=GxMm/(4R)²       (let x be the increase in mass)
divide GMm/R² from both sides,
1=x/16
x=16
therefore it should be multiplied 16 times.