How many moles of O2 are in the mixture?

Question

A gas mixture contains twice as many moles of O2 than N2. Addition fo 0.200 mol of argon to this mixture increases the pressure from 0.800 atm to 1.10 atm.

Answer 1

The partial pressure of 0.200 mol of Ar is (1.10 - 0.800) atm = 0.30 atm. Thus the original 0.800 atm contains 0.800*(2/3) mole or 0.533 mol gas mixture of O2 and N2.
Now, I do not understand what you mean by "twice as many moles of O2 than N2". If you mean "twice as many moles of O2 as N2", there would be 0.356 mole of O2 and 0.178 mole of N2. If, on the other hand, you mean "twice more moles of O2 than N2", there would be 0.400 mole of O2 and 0.133 mole of N2.