The volumes of two $\mathrm{HCl}$ solutions A(0.5N) and B(0.1 N) to be mixed for preparing 2 lit. of 0.2 N $\mathrm{HCl}$ solution 

Let x litre of A and (2-x) litre of B be mixed.

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

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

$(0.5-0.1)x = 0.4 - 0.2$

$0.4x = 0.2$

$x = 0.5L$

∴0.5 litre of A and 1.5 litre of B should be mixed.

Therefore, option A is the correct answer.