Explanation

(a) When space inside the toroid is filled with air,
$B_{0} = \mu_{0}\ H$
When filled with tungsten,
$B = \mu\ H = \mu_{0}\mu_{r}H = \mu_{0}\left( 1 + \mathcal{X}_{m} \right)H$
Percentage increase in magnetic field/ induction
$= \frac{(B - B_{0}) \times 100}{B_{0}} = \frac{\mu_{0}\mathcal{X}_{m} \times 100}{\mu_{0}H} = \mathcal{X}_{m} \times 100$
$= 6.8 \times 10^{- 5} \times 100 = 0.0068\%$.