Calculation of Power Consumption:

To calculate the cost of electric energy used in one month, we first need to determine the total power consumption of all the appliances.

Given:
- 6 fans, each consuming 50 W.
- 10 bulbs, each consuming 20 W.
- 2 TVs, each consuming 225 W.
- 1 motor consuming 250 W.

1. Calculate Power Consumption of Fans:
Power consumption of one fan = 50 W.
Power consumption of 6 fans = 50 W * 6 = 300 W.

2. Calculate Power Consumption of Bulbs:
Power consumption of one bulb = 20 W.
Power consumption of 10 bulbs = 20 W * 10 = 200 W.

3. Calculate Power Consumption of TVs:
Power consumption of one TV = 225 W.
Power consumption of 2 TVs = 225 W * 2 = 450 W.

4. Calculate Power Consumption of Motor:
Power consumption of motor = 250 W.

5. Calculate Total Power Consumption:
Total power consumption = Power consumption of fans + Power consumption of bulbs + Power consumption of TVs + Power consumption of motor
= 300 W + 200 W + 450 W + 250 W
= 1200 W.

Calculation of Monthly Energy Consumption:

To calculate the monthly energy consumption, we need to convert the power consumption into kilowatt-hours (kWh) and then multiply it by the number of hours used per day and the number of days in a month.

Given:
- Average usage per day = 8 hours.
- Number of days in a month = 30.

1. Convert Power Consumption to kWh:
Total power consumption = 1200 W = 1.2 kW.

2. Calculate Daily Energy Consumption:
Daily energy consumption = Total power consumption * Average usage per day = 1.2 kW * 8 hours = 9.6 kWh.

3. Calculate Monthly Energy Consumption:
Monthly energy consumption = Daily energy consumption * Number of days in a month = 9.6 kWh * 30 = 288 kWh.

Calculation of Cost of Electric Energy:

To calculate the cost of electric energy used in one month, we need to multiply the monthly energy consumption by the rate of the unit.

Given:
- Rate of unit = 6 rupees per kWh.

1. Calculate Cost of Electric Energy:
Cost of electric energy = Monthly energy consumption * Rate of unit = 288 kWh * 6 rupees/kWh = 1728 rupees.

Therefore, the cost of electric energy used in one month is 1728 rupees.