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%.