Did you take into consideration that the carbonate(IV) ion is
diprotic? (ie. Each CO3 2- ion accepts 2 H+ ions).
HCl and NaOH (which reacted with the excess HCl) are both
monoprotic, of course.
Check your sequence of steps :
Find mol of NaOH required for the back titration. Hence find mol
of HCl that reacted with the CaCO3 (ie. total HCl - HCl that
reacted with NaOH).
Then, divide this value by 2 (since carbonate(IV) is
diprotic) to find mol of CaCO3 present initially. Next, multiply
this value by the molar mass (or Mr) of CaCO3 to find the actual
sample mass of CaCO3 present initially.
Divide this value by the 1.068g impure sample, to find
percentage (by mass) purity of the CaCO3.
If you still get the same answer, it means the question is
flawed, eg. typo error in the question. The titre value of 273.1 ml
for the NaOH seems ridiculously large (imagine the size of the
burette required). It should more reasonably be 27.31 ml.