Why we need two resistors to control the gate voltage of a PUT transistor?
When the 15K resistor is left out, the gate of the SCR will be pulled down to the negative terminal (which is probably ground, but isn't shown in the schematic). When it is pulled down, the SCR will never turn on.

When the 27K resistor is left out, the gate of the SCR is pulled up. This will (almost) always turn on the SCR (provided that the terminal voltage (6V in case of this schematic) is high enough such that the gate trigger voltage is exceeded and the resistor (here 27K) is such that the gate trigger current is exceeded).

Using a voltage divider only makes sense if the terminal voltage can differ. Otherwise, for a fixed voltage, one can leave out the 27K resistor. For varying terminal voltage, tweaking the voltage divider determines at which terminal voltage the SRC is triggered.