Why battery voltage of DG pump varies from 12 volts to 15 volts

If battery is of 12volts in Diesel Generator Pump .Then why it varies from 12volts to 15volts

A generator's voltage varies by demand. The values you specify are in the proper operating range for a generator.

Voltage and amperage are inversely proportional. For the sake of example this means that if you running something at 12 volts, and it draws 5 amperes, it will draw 10 amperes at 6 volts.

Amperage is relative to heat energy, and the higher the amperes, the more heat an appliance will generate.

However, do not forget that things like motors are built to be run at certain voltages, and have a relatively narrow range, unless they are dual volatage capable, such as 120/240 AC motors.

A higher than rated voltage will damage the unit.

But I will reiterate, 15 volts is probably OK. It will vary according to the load and demand placed on the pump.