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Two unknown resistances X and Y are connected to left and right gaps of a meter bridge and the balancing point is obtained at 80cm from left. When a $10 Ω$ resistance is connected parallel to X, the balancing point is 50 cm from left. The values of X and Y respectively are

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$40 Ω, 9 Ω$

$30 Ω, 7.5 Ω$

$20 Ω, 6 Ω$

$10 Ω, 3 Ω$

answer is B.

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Detailed Solution

Initially

$\frac{X}{Y} = \frac{80}{20} \Rightarrow \frac{X}{Y} = 4;$

$\frac{10 x / (10 + x)}{y} = \frac{50}{100 - 50}$

$10 (4) = 10 + x \Rightarrow x = 30 Ω$

$\frac{x}{y} = 4$

$\Rightarrow y = 7.5 Ω$

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