Using KCL:

I1 + I2 = I $\hspace{2cm}$ …. (1)

And,

I2= 5/1200 = 4.167mA

I1= 5/600 = 8.333mA

Substituting in eq 1 we get,

4.167 + 8.333 = VA\R

Since,

VA= 35 – 5 =20

R= 2.4Kohms.

Using KVL:

Loop1:600I1 + (I1 + I2)R = 35 $\hspace{2cm}$ ….. (1)

Loop2: 600I1 = 1200I2

I1 = 2I2

Substituting in eq 1 we get,

(600 X 2I2) + (2I2 + I2)R = 35

1200I2 + 3I2R = 35

But,

I2= 5/1200 = 4.167mA

(1200 X 4.167 X 10-3) + 3(4.167 X 10-3R) = 35

R= 2.4Kohms.