6. (i) The following table presents the readings from an electricity meter with a 15-ampere capacity:
[Use the Service and Energy Charge of NEA from the given tariff rate.]

\begin{tabular}{|c|c|c|c|}
\hline [tex]$1^{\text{st}}$[/tex] Asoj & [tex]$1^{\text{st}}$[/tex] Kartik & [tex]$1^{\text{st}}$[/tex] Mangsir & [tex]$1^{\text{st}}$[/tex] Paush \\
\hline 2145 & 2352 & 2560 & 2845 \\
\hline
\end{tabular}

(a) Determine the service charge due for 325 units of electricity usage.

(b) Calculate the electricity consumption for the months of Asoj, Kartik, and Mangsir separately.

(c) Calculate the electricity bill for the month of Asoj.

(d) Ascertain the percentage difference in electricity usage between the highest and lowest consumption months among Asoj, Kartik, and Mangsir.

\begin{tabular}{|c|c|c|}
\hline \multirow[b]{2}{*}{\begin{tabular}{l}
KW/hr \\
(Unit)
\end{tabular}} & \multicolumn{2}{|c|}{15 Ampere} \\
\hline & \begin{tabular}{l}
Service \\
Charge
\end{tabular} & \begin{tabular}{l}
Energy \\
Charge
\end{tabular} \\
\hline [tex]$0-20$[/tex] & 50 & 4.00 \\
\hline [tex]$21-30$[/tex] & 75 & 6.50 \\
\hline [tex]$31-50$[/tex] & 75 & 8.00 \\
\hline [tex]$51-100$[/tex] & 100 & 9.50 \\
\hline [tex]$101-250$[/tex] & 125 & 9.50 \\
\hline Above 250 & 175 & 11.00 \\
\hline
\end{tabular}



Answer :

Certainly! Let's go through the problem step-by-step and provide detailed solutions to each part of the question.

### (a) Determine the service charge due for 325 units of electricity usage.

To determine the service charge and energy charge for 325 units:
- Given the rate table, for usage above 250 units, the service charge is ₹175 and the energy charge is ₹11.00 per unit.

Therefore, for 325 units:
- Service charge: ₹175
- Energy charge: 325 units × ₹11.00 = ₹3575.00

### (b) Calculate the electricity consumption for the months of Asoj, Kartik, and Mangsir separately.

We are given the meter readings:
- 1st Asoj: 2145
- 1st Kartik: 2352
- 1st Mangsir: 2560
- 1st Paush: 2845

To calculate the monthly consumption:
- Consumption in Asoj: Reading on 1st Kartik - Reading on 1st Asoj
- [tex]\(2352 - 2145 = 207\)[/tex] units
- Consumption in Kartik: Reading on 1st Mangsir - Reading on 1st Kartik
- [tex]\(2560 - 2352 = 208\)[/tex] units
- Consumption in Mangsir: Reading on 1st Paush - Reading on 1st Mangsir
- [tex]\(2845 - 2560 = 285\)[/tex] units

### (c) Calculate the electricity bill for the month of Asoj.

To calculate the bill for 207 units consumed in Asoj:
- Based on the rate table, for 101 to 250 units, the service charge is ₹125 and the energy charge is ₹9.50 per unit.
- Service charge: ₹125
- Energy charge: 207 units × ₹9.50 = ₹1966.50

Therefore, the total bill for Asoj:
- Total bill = Service charge + Energy charge
- ₹125 + ₹1966.50 = ₹2091.50

### (d) Ascertain the percentage difference in electricity usage between the highest and lowest consumption months among Asoj, Kartik, and Mangsir.

From the consumption calculated:
- Asoj: 207 units
- Kartik: 208 units
- Mangsir: 285 units

To find the percentage difference between the highest and lowest consumption months:
- Highest consumption: 285 units
- Lowest consumption: 207 units
- Percentage difference = [tex]\(\left(\frac{\text{Highest consumption} - \text{Lowest consumption}}{\text{Lowest consumption}}\right) \times 100\)[/tex]

[tex]\[ \frac{285 - 207}{207} \times 100 = 37.68\% \][/tex]

### Summary
Here are the summarized answers:
(a) Service charge due for 325 units: ₹175 and Energy charge: ₹3575.00
(b) Monthly consumptions:
- Asoj: 207 units
- Kartik: 208 units
- Mangsir: 285 units
(c) Electricity bill for the month of Asoj: ₹2091.50
(d) Percentage difference in electricity usage between highest and lowest month: 37.68%

These solutions provide a complete and detailed breakdown of how to approach and solve each part of the problem.