Question

why the oil does not mix in water however, oil and water becomes homogeneous if a sufficient quantity of detergent is added????

Answer 1

it is because of density difference between the quantity.
density of oil is less than water.. hence it float on water.
Now when detergent is added than it combinates the density difference and makes it homogeneous.

Answer 2

because the oils float on water because the molecules of oil are lossly packed but its molecules float because the molecules of oils is lossly packed but thin