Explanation

(b) The circuit can be simplified as follows
Applying $KCL$ at junction $A$
$i_{3} = i_{1} + i_{2}$ …(i)
Applying Kirchhoff’s voltage law for the loop $ABCDA$
$- 30i_{1} - 40i_{3} + 40 = 0$
$\Rightarrow - 30i_{1} - 40\left( i_{1} + i_{2} \right) + 40 = 0$
$\Rightarrow 7i_{1} + 4i_{2} = 4$ …(ii)
Applying Kirchhoff’s voltage law for the loop $ADEFA$
$- 40i_{2} - 40i_{3} + 80 + 40 = 0$
$\Rightarrow - 40i_{2} - 40\left( i_{1} + i_{2} \right) = - 120$
$\Rightarrow i_{1} + 2i_{2} = 3$ …(iii)
On solving equation (ii) and (iii) $i_{1} = - 0.4A$