If beaker a had 250ml of water beaker b had 500ml water are warmed from 10 celsius to 20 celsius what one requires more heat?

Because there is a greater volume of water in beaker B, the beaker would have to be heated for a longer period of time to reach the same temperature as beaker A. If your desire is to have both beakers warmed to the same temperature at the same time, beaker B would require the addition of more heat (because there is more water inside it).