Answer:
Option C
Explanation:
We have X+Y=1000Ω
Initially, $\frac{X}{l}=\frac{1000-X}{100-l}$ ..............(i)
When X and Y are interchanged, then
$\frac{1000-X}{l-10}=\frac{X}{100-(l-10)}$
OR $\frac{1000-X}{l-10}=\frac{X}{110-l}$ .........(ii)
From Eqs. (i) and (ii), we get
$\frac{100-l}{l}=\frac{l-10}{110-l}$
$\left(100-l\right)\left(110-l\right)$ = $\left(l-10\right)l$
$11000-100l -110l+l^{2}=l^{2}-10l$
$\Rightarrow$ $11000=200l$
$\therefore$ $l=55 cm$
Substituting the value of l in Eq. (i), we get
$\frac{X}{55}=\frac{1000-55}{100-55}$
$\Rightarrow$ 20X=11000
X= 550Ω