In a Wheatstone bridge (see figure) Resistance $P$ and $Q$ are approximately equal. When $R = 400\,\Omega ,$ the bridge is balanced. On interchanging $P$ and $Q,$ the value of $R,$ for balance is $405\,\Omega .$ The value of $X$ is close to ................. $ohm$
JEE MAIN 2019, Medium
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$\frac{P}{Q}=\frac{400}{s}$ .....$(1)$
and $\quad \frac{Q}{P}=\frac{405}{5}$ .......$(2)$
Solving $S^{2}=400 \times 405$
$\Rightarrow \quad S=402.5\, \Omega$
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