The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

= $P1+\frac{\frac{R}{2}}{100}2T-P=P1+\frac{1}{20}4-P=P\frac{21}{20}4-P$

Simple Interest on P at 10% for 2 years =  $\frac{PRT}{100}=\frac{P\times 10\times 2}{100}=\frac{P}{5}$

Given that difference between compound interest and simple interest = 124.05

  $P*\frac{21}{20}4-P-\frac{P}{5}=124.05$

=> $P\frac{21}{20}4-1-\frac{1}{5}=124.05$

 P=8000