Desk Light Electricity Cost Calculation
This solution breaks down the calculation for the electricity cost of a desk light under different usage scenarios and determines the percentage increase.
Initial Cost Calculation
First, calculate the energy consumed by the 40-watt desk light when used for 10 hours nightly over 180 days.
- Power of the light: 40 Watts (W)
- Convert Watts to Kilowatts (kW): $40 \text{ W} = \frac{40}{1000} \text{ kW} = 0.04 \text{ kW}$
- Initial daily usage: 10 hours (h)
- Number of days: 180 days
Calculate the total energy consumed in kilowatt-hours (kWh):
\begin{align*} \label{eq:1} \text{Total Energy (Initial)} &= \text{Power (kW)} \times \text{Daily Usage (h)} \times \text{Number of Days} \\ &= 0.04 \text{ kW} \times 10 \text{ h/day} \times 180 \text{ days} \\ &= 72 \text{ kWh}\end{align*}
Now, calculate the initial cost using the rate of ₹7 per kWh:
\begin{align*} \label{eq:2} \text{Initial Cost} &= \text{Total Energy (Initial)} \times \text{Rate per kWh} \\ &= 72 \text{ kWh} \times ₹7/\text{kWh} \\ &= ₹504\end{align*}
Cost Calculation with Increased Usage
Next, determine the cost when the desk light is used for 2 more hours each night.
- New daily usage: $10 \text{ h} + 2 \text{ h} = 12 \text{ hours}$
- Power of the light: 0.04 kW
- Number of days: 180 days
Calculate the new total energy consumed:
\begin{align*} \label{eq:3} \text{Total Energy (New)} &= \text{Power (kW)} \times \text{New Daily Usage (h)} \times \text{Number of Days} \\ &= 0.04 \text{ kW} \times 12 \text{ h/day} \times 180 \text{ days} \\ &= 86.4 \text{ kWh}\end{align*}
Calculate the new total cost:
\begin{align*} \label{eq:4} \text{New Cost} &= \text{Total Energy (New)} \times \text{Rate per kWh} \\ &= 86.4 \text{ kWh} \times ₹7/\text{kWh} \\ &= ₹604.8\end{align*}
Percentage Increase in Cost
Finally, calculate the percentage increase in the cost of energy consumption.
- Cost Increase: New Cost - Initial Cost
- Cost Increase: $₹604.8 - ₹504 = ₹100.8$
Use the formula for percentage increase:
\begin{align*} \label{eq:5} \text{Percentage Increase} &= \left( \frac{\text{Cost Increase}}{\text{Initial Cost}} \right) \times 100\% \\ &= \left( \frac{₹100.8}{₹504} \right) \times 100\% \\ &= 0.2 \times 100\% \\ &= 20\%\end{align*}
The initial cost is ₹504, and the percentage increase in cost is 20%.
Important Questions from Percentage
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