During an experiment with a metre bridge, the galvanometer shows a...

The unknown resistance is given by, $R = \left(\dfrac{x}{100 - x}\right)90$
Putting $x = 40 . 0cm$, $R = 60Ω$

For error analysis, $R = \left(\dfrac{40 . 0 \pm 0 . 1}{100 . 0 - \left(40 . 0 \pm 0 . 1\right)}\right) \times 90 = \left(\dfrac{40 . 0 \pm 0 . 1}{60 . 0 \pm 0 . 1}\right) \times 90$
In multiplication and division, fractional errors get added up.

Therefore, $\dfrac{∆ R}{R} = \dfrac{0 . 1}{40} + \dfrac{0 . 1}{60}$
$⇒ ∆ R = \dfrac{100}{\left(40\right)\left(60\right)} \times 0.1 \times 60$$= 0.25Ω$
Hence, $R = \left(60 \pm 0 . 25\right)Ω$