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Sagot :
Let's approach the problem step by step.
Part (i): Calculate the electricity charge for the month of Kartik.
1. Meter readings and units consumed:
- Initial meter reading on 1 Kartik: 1250 units
- Final meter reading on 1 Mansir: 1300 units
- Units consumed in the month of Kartik: [tex]\(1300 - 1250 = 50\)[/tex] units
2. Tariff rates:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Units (kWh)} & \text{Service charge} & \text{Energy charge} \\ \hline 0-20 & \text{Rs 75} & \text{Rs 5} \\ \hline 21-30 & \text{Rs 100} & \text{Rs 6.50} \\ \hline 31-50 & \text{Rs 100} & \text{Rs 8.00} \\ \hline 51-100 & \text{Rs 125} & \text{Rs 9.50} \\ \hline \end{array} \][/tex]
3. Calculate the charge:
- For the first 20 units:
- Service charge: Rs 75
- Energy charge: [tex]\(20 \times 5 = 100\)[/tex]
[tex]\[ \text{Total charge for first 20 units} = 75 + 100 = \text{Rs 175} \][/tex]
- For the next 10 units (21 to 30):
- Service charge: Rs 100
- Energy charge: [tex]\(10 \times 6.50 = 65\)[/tex]
[tex]\[ \text{Total charge for next 10 units} = 100 + 65 = \text{Rs 165} \][/tex]
- For the next 20 units (31 to 50):
- Service charge: Rs 100
- Energy charge: [tex]\(20 \times 8 = 160\)[/tex]
[tex]\[ \text{Total charge for next 20 units} = 100 + 160 = \text{Rs 260} \][/tex]
Total charge for Kartik:
[tex]\[ 175 + 165 + 260 = \text{Rs 600} \][/tex]
So, the electricity charge for the month of Kartik is Rs 600.
Part (ii): Calculate the electricity charge for the month of Asar.
1. Meter readings and units consumed:
- Initial meter reading on 1 Asar: 4040 units
- Final meter reading on 1 Saun: 4114 units
- Units consumed in the month of Asar: [tex]\(4114 - 4040 = 74\)[/tex] units
2. Tariff rates:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Units (kWh)} & \text{Service charge} & \text{Energy charge} \\ \hline 0-20 & \text{Rs 75} & \text{Rs 5} \\ \hline 21-30 & \text{Rs 100} & \text{Rs 6.50} \\ \hline 31-50 & \text{Rs 100} & \text{Rs 8.00} \\ \hline 51-100 & \text{Rs 125} & \text{Rs 9.50} \\ \hline \end{array} \][/tex]
3. Calculate the charge:
- For the first 20 units:
- Service charge: Rs 75
- Energy charge: [tex]\(20 \times 5 = 100\)[/tex]
[tex]\[ \text{Total charge for first 20 units} = 75 + 100 = \text{Rs 175} \][/tex]
- For the next 10 units (21 to 30):
- Service charge: Rs 100
- Energy charge: [tex]\(10 \times 6.50 = 65\)[/tex]
[tex]\[ \text{Total charge for next 10 units} = 100 + 65 = \text{Rs 165} \][/tex]
- For the next 20 units (31 to 50):
- Service charge: Rs 100
- Energy charge: [tex]\(20 \times 8 = 160\)[/tex]
[tex]\[ \text{Total charge for next 20 units} = 100 + 160 = \text{Rs 260} \][/tex]
- For the next 24 units (51 to 74):
- Service charge: Rs 125
- Energy charge: [tex]\(24 \times 9.50 = 228\)[/tex]
[tex]\[ \text{Total charge for next 24 units} = 125 + 228 = \text{Rs 353} \][/tex]
Total charge for Asar:
[tex]\[ 175 + 165 + 260 + 353 = \text{Rs 953} \][/tex]
So, the electricity charge for the month of Asar is Rs 953.
Summary:
1. For Kartik: Consumed units = 50, Charge = Rs 600
2. For Asar: Consumed units = 74, Charge = Rs 953
Part (i): Calculate the electricity charge for the month of Kartik.
1. Meter readings and units consumed:
- Initial meter reading on 1 Kartik: 1250 units
- Final meter reading on 1 Mansir: 1300 units
- Units consumed in the month of Kartik: [tex]\(1300 - 1250 = 50\)[/tex] units
2. Tariff rates:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Units (kWh)} & \text{Service charge} & \text{Energy charge} \\ \hline 0-20 & \text{Rs 75} & \text{Rs 5} \\ \hline 21-30 & \text{Rs 100} & \text{Rs 6.50} \\ \hline 31-50 & \text{Rs 100} & \text{Rs 8.00} \\ \hline 51-100 & \text{Rs 125} & \text{Rs 9.50} \\ \hline \end{array} \][/tex]
3. Calculate the charge:
- For the first 20 units:
- Service charge: Rs 75
- Energy charge: [tex]\(20 \times 5 = 100\)[/tex]
[tex]\[ \text{Total charge for first 20 units} = 75 + 100 = \text{Rs 175} \][/tex]
- For the next 10 units (21 to 30):
- Service charge: Rs 100
- Energy charge: [tex]\(10 \times 6.50 = 65\)[/tex]
[tex]\[ \text{Total charge for next 10 units} = 100 + 65 = \text{Rs 165} \][/tex]
- For the next 20 units (31 to 50):
- Service charge: Rs 100
- Energy charge: [tex]\(20 \times 8 = 160\)[/tex]
[tex]\[ \text{Total charge for next 20 units} = 100 + 160 = \text{Rs 260} \][/tex]
Total charge for Kartik:
[tex]\[ 175 + 165 + 260 = \text{Rs 600} \][/tex]
So, the electricity charge for the month of Kartik is Rs 600.
Part (ii): Calculate the electricity charge for the month of Asar.
1. Meter readings and units consumed:
- Initial meter reading on 1 Asar: 4040 units
- Final meter reading on 1 Saun: 4114 units
- Units consumed in the month of Asar: [tex]\(4114 - 4040 = 74\)[/tex] units
2. Tariff rates:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Units (kWh)} & \text{Service charge} & \text{Energy charge} \\ \hline 0-20 & \text{Rs 75} & \text{Rs 5} \\ \hline 21-30 & \text{Rs 100} & \text{Rs 6.50} \\ \hline 31-50 & \text{Rs 100} & \text{Rs 8.00} \\ \hline 51-100 & \text{Rs 125} & \text{Rs 9.50} \\ \hline \end{array} \][/tex]
3. Calculate the charge:
- For the first 20 units:
- Service charge: Rs 75
- Energy charge: [tex]\(20 \times 5 = 100\)[/tex]
[tex]\[ \text{Total charge for first 20 units} = 75 + 100 = \text{Rs 175} \][/tex]
- For the next 10 units (21 to 30):
- Service charge: Rs 100
- Energy charge: [tex]\(10 \times 6.50 = 65\)[/tex]
[tex]\[ \text{Total charge for next 10 units} = 100 + 65 = \text{Rs 165} \][/tex]
- For the next 20 units (31 to 50):
- Service charge: Rs 100
- Energy charge: [tex]\(20 \times 8 = 160\)[/tex]
[tex]\[ \text{Total charge for next 20 units} = 100 + 160 = \text{Rs 260} \][/tex]
- For the next 24 units (51 to 74):
- Service charge: Rs 125
- Energy charge: [tex]\(24 \times 9.50 = 228\)[/tex]
[tex]\[ \text{Total charge for next 24 units} = 125 + 228 = \text{Rs 353} \][/tex]
Total charge for Asar:
[tex]\[ 175 + 165 + 260 + 353 = \text{Rs 953} \][/tex]
So, the electricity charge for the month of Asar is Rs 953.
Summary:
1. For Kartik: Consumed units = 50, Charge = Rs 600
2. For Asar: Consumed units = 74, Charge = Rs 953
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