During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at…

The unknown resistance is given by, $R=\left(\frac{x}{100-x}\right)90$
Putting $x=40.0 \mathrm{cm}$, $R=60\mathrm{ }\mathrm{\Omega }$

For error analysis, $R=\left(\frac{40.0\pm 0.1}{100.0-\left(40.0\pm 0.1\right)}\right)\times 90=\left(\frac{40.0\pm 0.1}{60.0\pm 0.1}\right)\times 90$
In multiplication and division, fractional errors get added up.

Therefore, $\frac{∆R}{R}=\frac{0.1}{40}+\frac{{\displaystyle 0.1}}{{\displaystyle 60}}$
$\Rightarrow ∆R=\frac{100}{\left(40\right)\left(60\right)}\times 0.1\times 60$$=0.25\mathrm{ }\mathrm{\Omega }$
Hence, $R=\left(60\pm 0.25\right) \mathrm{\Omega }$