How to calculate value of R2 in this circuit?
simulate this circuit &ndash; Schematic created using CircuitLab

For the top resistors (all resistances calculated in 'k'):
$$ V_1 = 47 x  \tag 1 $$ 

For the bottom resistor:
$$ V_3 = 33 (x + 1) \tag 2 $$

From voltage drop across R1 and R3:

$$ V_1 + V_3 = 220 \tag 3 $$

$$ 47x + 33 (x+1) = 220 \tag 4 $$

$$ 80x = 220 - 33 \tag 5 $$

$$ x = \frac {187}{80} \tag 6 $$

Now you can work out V1 and therefore R2.