The volumes of two $HCl$ solutions A (0.5 M) and B (0.1 M) to be mixed for preparing 2 lit. of 0.2 M $HCl$ are

let x lit. of A and (2-x) lit. of B are mixed

$M_1{V}_1+M_2{V}_2=M_R(V_1+V_2)$

$0.5\times x+0.1(2-x)=0.2\times 2$

$x=\frac{0.2}{0.4}=0.5\mathrm{lit}.$

Y = 2 – x = 2 – 0.5 = 1.5 lit.