As the selling price is same
$Let$
$S.P \ be \ S$
$C.P \ of \ 1^{st} \ article \ be \ C_1$
$C.P \ of \ 2^{nd} \ article \ be \ C_2$
$Profit \ on \ 1^{st} \ article \ be \ P_1$
$Profit \ of \ 2^{nd} \ article \ be \ P_2$
$x = (P_{1} / C_{1})*100$
$P_1 = S - C_1$
$x = (S - C_1 / C_{1})*100$
$x/100 = S / C_{1} -1$
$C_{1} = 100.S / (100 + x)$
$y = (P_{2} / C_{2})*100$
$P_2 = S - C_2$
$y = (S - C_2 / C_{2})*100$
$y/100 = S / C_{2} -1$
$C_{2} = 100.S / (100 + y)$
$Total \ S.P = S + S = 2.S$
$Total \ C.P = C_1 + C_2$
$Total \ Profit(P) = 2.S - (C_1 + C_2)$
$z$ $= [P / (Total C.P)]*100$ \\ $z$ be the overall profit%
$z/100$ $= P / (C_1 + C_2)$
$= (2.S - ( C_1 + C_2 ) ) / (C_1 + C_2)$
$= 2.S / (C_1 + C_2) - 1$
$= (2.S / (100.S/(100 + x) + 100.S/(100 + y) ) ) - 1$
on solving we get,
$= [2.(100+x).(100+y)] / 100.[ (100 + x) + (100 + y) ] - 1$
$ = [ [2.100^2 + 200.x + 200.y + 2.x.y] - [100^2 + 100.x + 100^2 + 100.y] ] / 100.[ (100 + x) + (100 + y) ]$
$= [100.x + 100.y + 2.x.y] / 100.[ (100 + x) + (100 + y) ]$
$= [100.(x+y) + 2.x.y] / 100.[ (100 + x) + (100 + y) ]$
$z = [100.(x+y) + 2.x.y] / [ (100 + x) + (100 + y) ] $
same holds for overall loss%