If we use 365 days as the standard year then the times can be expressed as fractions of a year:
100/365=20/73; 150/365=30/73; 200/365=40/73.
The annual rate is 10.5%=0.105 so the fractions corresponding to these times are:
0.105(20/73)=2.1/73, 0.105(30/73)=3.15/73, 0.105(40/73)=4.2/73.
These reflect the interest, that is, the amounts required in the times specified are the principals plus interest, so we need to add 1 to each of these fractions to allow for the principal and interest combined. we get:
75.1/73, 76.15/73, 77.2/73. Next we divide the maturity values by these numbers to get the original principals invested days ago:
3000/(75.1/73)=$2,916.11, 4000/(76.15/73)=$3,834.54, 2000/(77.2/73)=$1,891.19.
CHECK
If these principals are correct, then we can prove them by applying simple interest to them. But let's do it in a slightly different way. We know that the annual rate is 10.5%. The daily rate is 10.5/365% or 0.000287871 as a decimal fraction.
After 100, 150 and 200 days this fraction becomes: 0.028767, 0.043151 and 0.057534. The correspond interest amounts are:
$83.89, $165.46, $108.81. when we add the principals we get:
$3,000, $4,000, $2,000. So the principals and interests are correct as calculated.