Answer :
Let's go step by step to solve the given questions:
### (a) Which formula can calculate the electricity consumption?
The electricity consumption in kilowatt-hours (kWh) can be calculated using the formula:
[tex]\[ \text{Electricity Consumption} = \frac{N \times P \times T}{1000} \][/tex]
where:
- [tex]\(N\)[/tex] is the number of items.
- [tex]\(P\)[/tex] is the power rating of the item in watts.
- [tex]\(T\)[/tex] is the number of hours used per day.
So, the correct option is:
a. [tex]\(\frac{N \times P \times T}{1000}\)[/tex]
### (b) What is the total units of electricity consumed by the family in a month assuming 1 month = 30 days?
First, we need to calculate the daily electricity consumption in kWh for each item, then sum these up, and finally, multiply by 30 to get the monthly consumption.
- Electric bulb (10 items, 100 W, 6 hours/day):
[tex]\[ \frac{10 \times 100 \times 6}{1000} = 6 \text{kWh/day} \][/tex]
- Electric bulb (15 items, 60 W, 8 hours/day):
[tex]\[ \frac{15 \times 60 \times 8}{1000} = 7.2 \text{kWh/day} \][/tex]
- Washing machine (1 item, 1000 W, 1 hour/day):
[tex]\[ \frac{1 \times 1000 \times 1}{1000} = 1 \text{kWh/day} \][/tex]
- Water pump (1 item, 500 W, 2 hours/day):
[tex]\[ \frac{1 \times 500 \times 2}{1000} = 1 \text{kWh/day} \][/tex]
- Rice cooker (1 item, 1500 W, 2 hours/day):
[tex]\[ \frac{1 \times 1500 \times 2}{1000} = 3 \text{kWh/day} \][/tex]
- Television (1 item, 100 W, 8 hours/day):
[tex]\[ \frac{1 \times 100 \times 8}{1000} = 0.8 \text{kWh/day} \][/tex]
- Geyser (1 item, 2000 W, 1 hour/day):
[tex]\[ \frac{1 \times 2000 \times 1}{1000} = 2 \text{kWh/day} \][/tex]
- Refrigerator (1 item, 125 W, 24 hours/day):
[tex]\[ \frac{1 \times 125 \times 24}{1000} = 3 \text{kWh/day} \][/tex]
Now, summing up the daily consumption:
[tex]\[ 6 + 7.2 + 1 + 1 + 3 + 0.8 + 2 + 3 = 24 \text{kWh/day} \][/tex]
Monthly consumption:
[tex]\[ 24 \text{kWh/day} \times 30 \text{days} = 720 \text{kWh} \][/tex]
### (c) Calculate the electricity bill for the given month, if the cost of electricity is as indicated in the above table.
The monthly consumption is 720 kWh. The tariff structure is provided in the table, and we need to calculate the total bill step by step.
1. Units 0-20:
- Total service charge: Rs. 125
- Energy charge: 20 units [tex]\(\times\)[/tex] Rs. 6.00 = Rs. 120
2. Units 21-30:
- Energy charge: 10 units [tex]\(\times\)[/tex] Rs. 6.50 = Rs. 65
3. Units 31-50:
- Energy charge: 20 units [tex]\(\times\)[/tex] Rs. 8.00 = Rs. 160
4. Units 51-150:
- Total service charge: Rs. 150
- Energy charge: 100 units [tex]\(\times\)[/tex] Rs. 9.50 = Rs. 950
5. Units 151-250:
- Total service charge: Rs. 200
- Energy charge: 100 units [tex]\(\times\)[/tex] Rs. 9.50 = Rs. 950
6. Above 250 units:
- Total service charge: Rs. 250
- Energy charge: 470 units [tex]\(\times\)[/tex] Rs. 11.00 = Rs. 5170
Summarizing the total charges:
- Energy Charge = Rs. 120 + Rs. 65 + Rs. 160 + Rs. 950 + Rs. 950 + Rs. 5170 = Rs. 7425.5
- Service Charge = Rs. 250
Total bill:
[tex]\[ 7425.5 + 250 = 7675.5 \text{ Rs.} \][/tex]
Thus, the detailed bill for the month is Rs. 7675.5.
### (a) Which formula can calculate the electricity consumption?
The electricity consumption in kilowatt-hours (kWh) can be calculated using the formula:
[tex]\[ \text{Electricity Consumption} = \frac{N \times P \times T}{1000} \][/tex]
where:
- [tex]\(N\)[/tex] is the number of items.
- [tex]\(P\)[/tex] is the power rating of the item in watts.
- [tex]\(T\)[/tex] is the number of hours used per day.
So, the correct option is:
a. [tex]\(\frac{N \times P \times T}{1000}\)[/tex]
### (b) What is the total units of electricity consumed by the family in a month assuming 1 month = 30 days?
First, we need to calculate the daily electricity consumption in kWh for each item, then sum these up, and finally, multiply by 30 to get the monthly consumption.
- Electric bulb (10 items, 100 W, 6 hours/day):
[tex]\[ \frac{10 \times 100 \times 6}{1000} = 6 \text{kWh/day} \][/tex]
- Electric bulb (15 items, 60 W, 8 hours/day):
[tex]\[ \frac{15 \times 60 \times 8}{1000} = 7.2 \text{kWh/day} \][/tex]
- Washing machine (1 item, 1000 W, 1 hour/day):
[tex]\[ \frac{1 \times 1000 \times 1}{1000} = 1 \text{kWh/day} \][/tex]
- Water pump (1 item, 500 W, 2 hours/day):
[tex]\[ \frac{1 \times 500 \times 2}{1000} = 1 \text{kWh/day} \][/tex]
- Rice cooker (1 item, 1500 W, 2 hours/day):
[tex]\[ \frac{1 \times 1500 \times 2}{1000} = 3 \text{kWh/day} \][/tex]
- Television (1 item, 100 W, 8 hours/day):
[tex]\[ \frac{1 \times 100 \times 8}{1000} = 0.8 \text{kWh/day} \][/tex]
- Geyser (1 item, 2000 W, 1 hour/day):
[tex]\[ \frac{1 \times 2000 \times 1}{1000} = 2 \text{kWh/day} \][/tex]
- Refrigerator (1 item, 125 W, 24 hours/day):
[tex]\[ \frac{1 \times 125 \times 24}{1000} = 3 \text{kWh/day} \][/tex]
Now, summing up the daily consumption:
[tex]\[ 6 + 7.2 + 1 + 1 + 3 + 0.8 + 2 + 3 = 24 \text{kWh/day} \][/tex]
Monthly consumption:
[tex]\[ 24 \text{kWh/day} \times 30 \text{days} = 720 \text{kWh} \][/tex]
### (c) Calculate the electricity bill for the given month, if the cost of electricity is as indicated in the above table.
The monthly consumption is 720 kWh. The tariff structure is provided in the table, and we need to calculate the total bill step by step.
1. Units 0-20:
- Total service charge: Rs. 125
- Energy charge: 20 units [tex]\(\times\)[/tex] Rs. 6.00 = Rs. 120
2. Units 21-30:
- Energy charge: 10 units [tex]\(\times\)[/tex] Rs. 6.50 = Rs. 65
3. Units 31-50:
- Energy charge: 20 units [tex]\(\times\)[/tex] Rs. 8.00 = Rs. 160
4. Units 51-150:
- Total service charge: Rs. 150
- Energy charge: 100 units [tex]\(\times\)[/tex] Rs. 9.50 = Rs. 950
5. Units 151-250:
- Total service charge: Rs. 200
- Energy charge: 100 units [tex]\(\times\)[/tex] Rs. 9.50 = Rs. 950
6. Above 250 units:
- Total service charge: Rs. 250
- Energy charge: 470 units [tex]\(\times\)[/tex] Rs. 11.00 = Rs. 5170
Summarizing the total charges:
- Energy Charge = Rs. 120 + Rs. 65 + Rs. 160 + Rs. 950 + Rs. 950 + Rs. 5170 = Rs. 7425.5
- Service Charge = Rs. 250
Total bill:
[tex]\[ 7425.5 + 250 = 7675.5 \text{ Rs.} \][/tex]
Thus, the detailed bill for the month is Rs. 7675.5.
