Let two resistors 10 ohm and 5 ohm connected in series with a battery of potential difference of V volts.
Equivalent resistance, R = R1 + R2 = 10 + 5 = 15 ohms
Current through both the resistances, I = V/R = V/15 amperes.
potential difference through resistor R1 = 10 ohms is V1 = I R1 = (V/15) 10 volts.
potential difference through resistor R2 = 5 ohms is V2 = I R2 = (V/15) 5 volts.