Mahesh Godavarti
1

Let's set up the equations appropriately.


Let I_i be the current through R_i . I will assume the currents flowing top to bottom and left to right.


Then we have:


24 = I_1 R_1 + I_4 R_4 = I_2 R_2 + I_5 R_5

I_1 R_1 + I_3 R_3 = I_2 R_2

I_1 = I_3 + I_4

I_5 = I_2 + I_3


We have five equations in five unknowns. Let's solve them!


24 = I_1 R_1 + R_4 (I_1 - I_3) = I_2 R_2 + R_5 (I_2 + I_3)


24 = I_2 (R_2 + R_5) + I_3 R_5

24 = I_2 R_2 - I_3 R_3 - R_4 I_3 + R_4 (I_2 R_2 - I_3 R_3 ) / R_1 \implies 24 = I_2 R_2 (1 + R_4 / R_1) - I_3 R_3 (1 + R_4 / R_1) \implies 24 R_1 / (R_1 + R_4) = I_2 R_2 + I_3 R_3


Therefore,

24 = 300 I_2 + 250 I_3

8 = 50 I_2 + 100 I_3


Therefore, I_3 = 24 / (350) A, I_2 = 12 / 75 = 4/ 25 A .


Solve, for the rest.