On interchanging, the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 kΩ. How much was the resistance on the left slot before interchanging the resistances?

# On interchanging, the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\text{\hspace{0.17em}}\mathrm{k\Omega }$. How much was the resistance on the left slot before interchanging the resistances?

1. A

$910\text{\hspace{0.17em}}\mathrm{\Omega }$

2. B

$990\text{\hspace{0.17em}}\mathrm{\Omega }$

3. C

$505\text{\hspace{0.17em}}\mathrm{\Omega }$

4. D

$550\text{\hspace{0.17em}}\mathrm{\Omega }$

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$\frac{\mathrm{X}}{\mathrm{R}}=\frac{\mathrm{\ell }}{\left(100-\mathrm{\ell }\right)},\frac{\mathrm{R}}{\mathrm{X}}=\frac{\mathrm{\ell }-10}{10-\mathrm{\ell }}$
And $\mathrm{X}+\mathrm{R}=1000\mathrm{\Omega }$