In order to meet a certain octane number specification,it is necessary to produce a motor gasoline with 80% w/w i-octane and 20% w/w n-heptane.What volume flow rates of high-octane gasoline (90%w/w i-octane and 10% w/w n-heptane) and low octane gasoline (65% w/w i octane and 35% w/w n-heptane) must be blended to get 100m3/h of the desired gasoline?

So I know mass is conserved and not volume.So m1+m2=100.So p1v1 + p2v2=100 where p is the guven density.But how to get the second equation?

 

You need the partial molar volume of each component in the final solution. The gross approximation is that they do not change upon mixing. That will get you close, but I'm fairly sure the point of the question is to demonstrate the impact of the phenomena whereby they are not constant. For instance when you mix water and alcohol, the final volume is notably (4%? I forget) less than the sum of the parts. You'll need to find data about such mixtures.