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When the Wheatstone bridge shown in the figure is used to find the value of resistor $R_{X}$, the galvanometer $G$ indicates zero current when $R_{1}=50\Omega, R_{2}=65\Omega$ and $R_{3}=100\Omega$. If $R_{3}$ is known with $±5$% tolerance on its nominal value of $100 \Omega$ , what is the range of $R_{X}$ in Ohms?

- $[123.50, 136.50]$
- $[125.89, 134.12]$
- $[117.00, 143.00]$
- $[120.25, 139.75]$

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