In the given circuit Ammeter reading is same when both switches$S_1$ , $S_2$ are closed or opened. The value of resistance R is

When circuit is opened $i_1=\frac{1.5}{300+100+50}=\frac{1.5}{450}=\frac{1}{300}$

When circuit is closed Total current $i=\frac{1.5}{300+\frac{100R}{100+R}}=\frac{1.5(100+R)}{300\times 100+400R}$

Current through $100\mathrm{\Omega };i_2=\frac{iR}{100+R}$

$\text{ But }{i}_1=i_2$

$\frac{1}{300}=\frac{i\times R}{100+R}=\frac{1.5(100+R)}{300\times 100\times 400R}\times \frac{R}{100+R}$

$\therefore R=600\mathrm{\Omega }$