If all gas mixtures are occupying the same volume at the same temperature, partial pressures of A and C are:
P
A
= n
A
(RT/V)
P
C
= n
C
(RT/V)
And consequently P
A
/P
C
= n
A
/n
C
. Remember that X
A
/X
C
= n
A
/n
C
.