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A resistance of $2 Ω$ is connected across one gap of a meter bridge (the length of the wire is 100cm) and an unknown resistance greater than $2 Ω$ is connected across the other gap. When these resistances are inter-charged, then balance point shifts by 20cm. Neglecting any correction, the unknown resistance is $___________Ω$

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answer is 3.

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Detailed Solution

Applying $\frac{P}{Q} = \frac{R}{S}$
We have $\frac{2}{R} = \frac{X}{100 - X} \to (1)$

$\frac{R}{2} = \frac{X + 20}{100 - (X + 20)} = \frac{X + 20}{80 - X} \to (2)$

On solving equations $(1) & (2),$ we get $R = 3 Ω$

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