let applied voltage be x V

so, by kirchoffs laws, we have :

let I₁ be current in case 1 and I₂ be in case 2

so acroess voltmeters , we have    198 = 900I_{1      . .. (1)}

                                               180 = 900I₂     ... (2)

and for whole circuit, we have : x - 198 = I₁(R₁+900)        ... (3)

                                            x - 180 = I₂(2R₁+900)       ... (4)

on solving eqns, 1 to 4 , we have

x = 220V

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Ramesh
IIT Kgp - 05 batch