Answer :
To solve the given problem, we will follow several steps methodically. Below is a step-by-step solution.
### (2) Daily Electricity Consumption of 5 TVs
Given:
- Number of TVs: 5
- Power rating of each TV: 150 watts
- Operating hours per day: 4 hours
Calculation:
The total daily electricity consumption can be found by multiplying the number of TVs by the power rating of each TV and then by the number of hours they operate daily.
[tex]\[ \text{Total Daily Electricity Consumption} = \text{Number of TVs} \times \text{Power Rating} \times \text{Hours per Day} \][/tex]
[tex]\[ \text{Total Daily Electricity Consumption} = 5 \times 150 \times 4 = 3000 \text{ watts} \][/tex]
### (3) Watts per Unit of Electricity
1 unit of electricity is equivalent to 1000 watts.
### (4) Monthly Charge for Using the TVs
Given:
- Per unit charge: Rs. 13
- Days per month: 30 days
Calculations:
First, convert the daily electricity consumption in watts to units. Since 1 unit = 1000 watts:
[tex]\[ \text{Daily Consumption in Units} = \frac{3000 \text{ watts}}{1000 \text{ watts/unit}} = 3 \text{ units} \][/tex]
Next, calculate the monthly consumption by multiplying the daily consumption by the number of days in a month.
[tex]\[ \text{Monthly Consumption in Units} = 3 \text{ units/day} \times 30 \text{ days/month} = 90 \text{ units} \][/tex]
Finally, calculate the monthly charge by multiplying the monthly consumption in units by the per unit charge.
[tex]\[ \text{Monthly Charge} = 90 \text{ units} \times Rs. 13/\text{unit} = Rs. 1170 \][/tex]
### Studying the Table and Completing the Calculations
| SV | Electric Appliance | Number of sets | Capacity (watts) | Used Time (hours) | Consumed Units |
|-----|---------------------|----------------|-------------------|-------------------|-------------------|
| th. | Television | 2 | 100 | 5 | 1.0 |
| 2 | Iron | 3 | 2000 | 0.5 | 3.0 |
| 3. | Bulb | 2 | 15 | 8 | 0.24 |
| ± | Rice Cooker | 1 | 1000 | 1 | 1.0 |
| 5. | Total | - | - | - | 5.24 |
#### Calculation of Consumed Units for Each Appliance:
For each appliance, the consumed units can be calculated by:
[tex]\[ \text{Consumed Units} = \left(\text{Number of Sets} \times \text{Capacity (watts)} \times \text{Used Time (hours)}\right) \div 1000 \][/tex]
- Television:
[tex]\[ \left(2 \times 100 \times 5\right) \div 1000 = 1.0 \text{ units} \][/tex]
- Iron:
[tex]\[ \left(3 \times 2000 \times 0.5\right) \div 1000 = 3.0 \text{ units} \][/tex]
- Bulb:
[tex]\[ \left(2 \times 15 \times 8\right) \div 1000 = 0.24 \text{ units} \][/tex]
- Rice Cooker:
[tex]\[ \left(1 \times 1000 \times 1\right) \div 1000 = 1.0 \text{ units} \][/tex]
- Total Consumption:
Sum up the units consumed by all appliances:
[tex]\[ 1.0 + 3.0 + 0.24 + 1.0 = 5.24 \text{ units} \][/tex]
### (a) Payment at Rs. 15 per Unit
If the table shows the consumption of electricity by a tenant, the cost can be calculated as follows:
Given:
- Per unit charge: Rs. 15
- Total consumed units: 5.24 units
Calculation:
[tex]\[ \text{Total Cost} = 5.24 \text{ units} \times Rs. 15/\text{unit} = Rs. 78.6 \][/tex]
Thus, the tenant would pay Rs. 78.6 for the electricity consumption as shown in the table.
### (2) Daily Electricity Consumption of 5 TVs
Given:
- Number of TVs: 5
- Power rating of each TV: 150 watts
- Operating hours per day: 4 hours
Calculation:
The total daily electricity consumption can be found by multiplying the number of TVs by the power rating of each TV and then by the number of hours they operate daily.
[tex]\[ \text{Total Daily Electricity Consumption} = \text{Number of TVs} \times \text{Power Rating} \times \text{Hours per Day} \][/tex]
[tex]\[ \text{Total Daily Electricity Consumption} = 5 \times 150 \times 4 = 3000 \text{ watts} \][/tex]
### (3) Watts per Unit of Electricity
1 unit of electricity is equivalent to 1000 watts.
### (4) Monthly Charge for Using the TVs
Given:
- Per unit charge: Rs. 13
- Days per month: 30 days
Calculations:
First, convert the daily electricity consumption in watts to units. Since 1 unit = 1000 watts:
[tex]\[ \text{Daily Consumption in Units} = \frac{3000 \text{ watts}}{1000 \text{ watts/unit}} = 3 \text{ units} \][/tex]
Next, calculate the monthly consumption by multiplying the daily consumption by the number of days in a month.
[tex]\[ \text{Monthly Consumption in Units} = 3 \text{ units/day} \times 30 \text{ days/month} = 90 \text{ units} \][/tex]
Finally, calculate the monthly charge by multiplying the monthly consumption in units by the per unit charge.
[tex]\[ \text{Monthly Charge} = 90 \text{ units} \times Rs. 13/\text{unit} = Rs. 1170 \][/tex]
### Studying the Table and Completing the Calculations
| SV | Electric Appliance | Number of sets | Capacity (watts) | Used Time (hours) | Consumed Units |
|-----|---------------------|----------------|-------------------|-------------------|-------------------|
| th. | Television | 2 | 100 | 5 | 1.0 |
| 2 | Iron | 3 | 2000 | 0.5 | 3.0 |
| 3. | Bulb | 2 | 15 | 8 | 0.24 |
| ± | Rice Cooker | 1 | 1000 | 1 | 1.0 |
| 5. | Total | - | - | - | 5.24 |
#### Calculation of Consumed Units for Each Appliance:
For each appliance, the consumed units can be calculated by:
[tex]\[ \text{Consumed Units} = \left(\text{Number of Sets} \times \text{Capacity (watts)} \times \text{Used Time (hours)}\right) \div 1000 \][/tex]
- Television:
[tex]\[ \left(2 \times 100 \times 5\right) \div 1000 = 1.0 \text{ units} \][/tex]
- Iron:
[tex]\[ \left(3 \times 2000 \times 0.5\right) \div 1000 = 3.0 \text{ units} \][/tex]
- Bulb:
[tex]\[ \left(2 \times 15 \times 8\right) \div 1000 = 0.24 \text{ units} \][/tex]
- Rice Cooker:
[tex]\[ \left(1 \times 1000 \times 1\right) \div 1000 = 1.0 \text{ units} \][/tex]
- Total Consumption:
Sum up the units consumed by all appliances:
[tex]\[ 1.0 + 3.0 + 0.24 + 1.0 = 5.24 \text{ units} \][/tex]
### (a) Payment at Rs. 15 per Unit
If the table shows the consumption of electricity by a tenant, the cost can be calculated as follows:
Given:
- Per unit charge: Rs. 15
- Total consumed units: 5.24 units
Calculation:
[tex]\[ \text{Total Cost} = 5.24 \text{ units} \times Rs. 15/\text{unit} = Rs. 78.6 \][/tex]
Thus, the tenant would pay Rs. 78.6 for the electricity consumption as shown in the table.
