To determine the cost of running five 60 W lamps and four 100 W lamps for 20 hours, we need to follow a series of steps to calculate the total energy consumed and then convert that into a cost based on the given rate of electrical energy. ### Step-by-Step Explanation 1. **Calculate the total power consumption of the lamps:** - First, we need to find the total power consumed by the 60 W lamps and the 100 W lamps. - For the five 60 W lamps: \[ \text{Total power for 60 W lamps} = 5 \text{ lamps} \times 60 \text{ W/lamp} = 300 \text{ W} \] - For the four 100 W lamps: \[ \text{Total power for 100 W lamps} = 4 \text{ lamps} \times 100 \text{ W/lamp} = 400 \text{ W} \] - Now, add the power consumption of both types of lamps: \[ \text{Total power} = 300 \text{ W} + 400 \text{ W} = 700 \text{ W} \] 2. **Convert power from watts to kilowatts:** - Since the cost of electricity is given in kilowatt-hours (kWh), we need to convert watts to kilowatts: \[ \text{Total power in kW} = \frac{700 \text{ W}}{1000} = 0.7 \text{ kW} \] 3. **Calculate the total energy consumed over 20 hours:** - Energy consumed (in kWh) can be calculated using the formula: \[ \text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (hours)} \] - Substituting the values we have: \[ \text{Energy} = 0.7 \text{ kW} \times 20 \text{ hours} = 14 \text{ kWh} \] 4. **Calculate the total cost of the energy consumed:** - The cost of running the lamps can be calculated by multiplying the total energy consumed by the cost per kWh: \[ \text{Cost} = \text{Energy (kWh)} \times \text{Cost per kWh} \] - Given that the cost per kWh is #10.00: \[ \text{Cost} = 14 \text{ kWh} \times 10.00 \text{ #/kWh} = 140.00 \] ### Conclusion The total cost of running the lamps for 20 hours is **#140.00**. Therefore, the correct option is **D**. ### Explanation of Other Options - **Option A: #280.00** - This value could be derived from a miscalculation, possibly by doubling the correct cost or misinterpreting the number of hours or power. - **Option B: #160.00** - This might result from an incorrect calculation of energy consumed or a misunderstanding of the cost per kWh. - **Option C: #120.00** - This could arise from an error in calculating the total power or the time duration. ### Revision Summary - Calculate total power by summing the power of all lamps. - Convert watts to kilowatts for energy calculations. - Use the formula \( \text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (hours)} \). - Multiply total energy by the cost per kWh to find the total cost.