A feed to a distillation column is $F=200$kmo$\frac{l}{h}r,$ with composition $x_a=0\mathrm{.}15$;$x_b=0\mathrm{.}15,x_c=0\mathrm{.}7.$ The bottom product of the distillation column is Bkmo$\frac{l}{h}r,$ with a composition of $x_a=0\mathrm{.}03$;$x_b=0\mathrm{.}2$;$x_c=0\mathrm{.}77.$ The top stream is Tkmo$\frac{l}{h}r,$ with unknown composition $y_a$;$y_b$;$y_c.$ The top stream is blended with a stream of $100$kmo$\frac{l}{h}r$ consisting of $45\%$A and $55\%$ B $($molar fractions$),$ to form a product P$.$ Product $P$ has $20\%$ C $($molar fraction.

Draw a schematic of the process, annotate all known and unknown values and solve the problem.