Imagine a system beginning with 15%Q and a 30%P/70%Q eutectic. Cool and fractionate the system until just at the point all the least abundant mineral melts. What is the composition of the two fractions, and at what temperature will this occur?
Answers: For both P and Q to melt together we must be at the eutectic. Therefore, the temperature at which all this is taking place is the eutectic, about 1230o.
And since they melt in the eutectic ratio until all of the least abundant is gone (here Q), and the question asks the composition at the point the least abundant component finally all melts this must be at the eutectic ratio. That is, 30%P/70%Q.