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It's all about the capacity of the system.  You can't magically produce energy out of thin air.  You have to calculate the energy that your project requires and then choose a system that can generate at least that amount of energy from the sunlight.
The best you are going to get charging a battery with that setup is a 2.5 amp charging current.  Let's say you are able to charge your battery for eight hours.  8 * 2.5 = 20 amp-hours into the battery.   In using that same energy,  his 100 watt lamp would draw 7.25 amps,  so we can calculate 20 amp-hours / 7.25 amps = 2.75 hours.  His lamp would last 2.75 hours after an eight hour charge from that system.
To last 12 hours, he would need more than four times the capacity of that system, which brings us back to the 200 watt panel and the correctly sized battery that I described earlier.