In this question they have taken current in the potentiometer wire to measure the resistant. According to me there is no way we can find X because connecting it in parallel should not have any affect on the balancing length.
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rishabh gupta
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1Yes, the circuit does look totally wrong if this is supposed to be a balanced bridge. The only thing this can measure is the voltage of the second battery under load of the two resistors. – CuriousOne Jan 13 '16 at 19:59
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I ageer with @CuriousOne - assuming that the impedance of the galvanometer is very high, you are measuring the "voltage under load" of the second voltage source. If the known and unknown resistor were in series, with the gal I at their junction, it would be a different thing. Almost certainly a printing/ proofreading error. – Floris Jan 13 '16 at 21:44