Volume of x solution is 360. The ratio of pure x in the solvent is 6:9. 360/(6+9)=24 units so there are 6×24=144 units of pure x in the solution, and 216 units of solvent.
Volume of y solution is 300. The ratio of pure y in the solvent is 3:7. 300/(3+7)=30 units so there are 3×30=90 units of pure y in the solution, and 210 units of solvent.
If the solutions are mixed (unequal volumes) we have a volume of 360+300=660 units, in which there are 144 units of x and 90 units of y (234 units of x and y). The ratio of the combined x and y in solution is 234/660=39:110. Assuming x and y combine to make z (no residual x or y or any other substance), we would have 234 units of z in a volume of 660 units. If we take an equal volume V of x and y and mix them we get the solution z, which has a volume 2V. The amount of x in V is 2V/3 and the amount of y in V is 3V/7. The ratio of x in the mixture is (2V/3)/(2V)=1:3, and that for y is (3V/7)/2V=3:14.
If x and y combine completely to make z, then the amount of z in solution is 2V/3+3V/7=14V/21+9V/21=23V/21 and the ratio of z in the mixture is (23V/21)/(2V)=23:42. If we have 10 units of the mixture, we can work out how much of the mixture is z=10(23/42)=115/21 units (about 5.48 units).
If equal volumes of x and y are required to make z then mixing 360 units of x solution with 300 units of y solution will give us a total volume of 660 units. There is a surplus of x in solution, because there are 144 units of x compared with 90 units of y. So we would end up with 180 units of z (90 units each of x and y) and 144-90=54 units of x. The final solution would be 180 units of z, 54 units of x, and 660-234=426 units of solvent. Therefore we would have 180/660 or ratio 3:11 of z in solution and 54/660=9:110 of x. If we had only 10 units of this concentration, the amount of z would be 10(3/11)=30/11=2.73 (approx) units of z.
The answer to this question depends on how it's interpreted.