Simple Interest =$\dfrac{PRT}{100}$ = $\dfrac{900 \times 10 \times 1}{100} $= Rs.90

Amount after 1 year on Rs.900 at 10% per annum when interest is reckoned half-yearly

=P $\left(1 + \dfrac{\left(R/2\right)}{100}\right)^2T$ = 900$\left(1 + \dfrac{(10/2)}{100}\right)^{2 \times 1}$ = 900$\left(1 + \dfrac{5}{100}\right)^{2}$ = 900$\left(\dfrac{105}{100}\right)^{2}$

$= \dfrac{900\times 105 \times 105}{100 \times 100}$ = Rs.992.25

Compound Interest = 992.25 - 900 = 92.25

Required difference between simple interest and compound interest = 92.25 - 90 = Rs.2.25