The power (in watt) is defined as the multiplication of the voltage and the current
[tex]P=I*V[/tex]
Then, the current equals [tex]P/V=\frac{50}{12.6}=3.9683 Amp\\[/tex]
Because the certain fully charged deep-cycle lead acid storage battery is rated for 12.6 v and 100 ampere hours (the same voltage)
so, the time which the electronics can be operated from the battery without recharging = [tex]\frac{100 Amp.hour}{3.9683Amp}=25.2 hours[/tex]