claims paid + loss adjustments=¾ (75%) of premium=¾ of 3456=2592.
To make the loss ratio 55% for the same claims costs (i.e., 2592):
2592/premium=0.55 (55% loss ratio), premium=2592/0.55=4712.73.
The premium is therefore increased from 3456 to 4712.72, an increase of 1256.73.
As a percentage this is 1256.73/3456=4/11=36.3636% (400/11%).
GENERALISATION
claims paid + loss adjustments=r1% of premium P1=r1P1/100.
To make the loss ratio r2% for the same claims costs:
(r1P1/100)/P2=r2%, P2=r1P1/r2.
The premium is therefore increased from P1 to P2, an increase of P2-P1, or 100(P2-P1)/P1%.