Total volume of the sample =

Let the volume of oil be x
Volume of vinegar be y
x + y =
------------------Equation-1
Density of oil = 0.909

Density of vinegar = 1.056

Mass of oil = x * 0.909
=0.909x
Mass of vinegar = y * 1.056
=1.056y
Total mass of sample = 188 g
0.909x + 1.056y=188 ------------------ Equation -2
Using the equation x + y = 196 ==> x = 196 - y in equation-2 we get,
0.909x + 1.056y=188
0.909(196 - y) + 1.056y=188
178.196 - 0.909 y + 1.056 y = 188
178.196 + 0.147 y = 188
0.147 y = 9.831
y = 66.9

Finding out the value of x :
x + y = 196
x + 66.9 = 196
x = 129.1

Therefore, the volume of oil = 129.1
and volume of vinegar = 66.9
