Answer : Option D

Explanation :

Let the sum be P
Compound Interest on P at 10% for 2 years when interest is compounded half-yearly
$MF#%=\text{P}\left(1 + \dfrac{\text{(R/2)}}{100}\right)^\text{2T} - \text{P}
= \text{P}\left(1 + \dfrac{(10/2)}{100}\right)^{2 \times 2} - \text{P} = \text{P}\left(1 + \dfrac{1}{20}\right)^4- \text{P} = \text{P}\left(\dfrac{21}{20}\right)^4- \text{P}\\\\ \text{Simple Interest on P at 10% for 2 years = }\dfrac{\text{PRT}}{100} = \dfrac{\text{P} \times 10 \times 2}{100}=\dfrac{\text{P}}{5}$MF#%
Given that difference between compound interest and simple interest = 124.05
$MF#%=> \text{P}\left(\dfrac{21}{20}\right)^4- \text{P} - \dfrac{\text{P}}{5} = 124.05\\\\ => \text{P}\left[\left(\dfrac{21}{20}\right)^4 - 1 - \dfrac{1}{5}\right]= 124.05\\\\ => \text{P}\left[\dfrac{194481}{160000} - 1 - \dfrac{1}{5}\right]= 124.05\\\\ => \text{P}\left[\dfrac{194481 - 160000 - 32000}{160000}\right]= 124.05\\\\ => \text{P}\left[\dfrac{2481}{160000}\right]= 124.05\\\\ => \text{P} = \dfrac{124.05 \times 160000}{2481}=\dfrac{160000}{20}=8000$MF#%