Answer :
### 1. Defining "Tariff"
A tariff is a system or schedule of fees or taxes that are applied to particular goods or services. In the context of water usage, it refers to the pricing structure that the municipality charges households for their water consumption based on different usage levels. Essentially, a tariff system determines how much residents pay per unit of water consumed.
### 2. Calculate the Tariffs Excluding VAT for Water Consumption Between 10 kl and 20 kl
To determine the tariffs excluding VAT:
- For water consumption between 10 kilolitres (kl) and 20 kl, the tariff is R5.20 per kilolitre.
- Since there are 15% VAT included in the provided tariff, we can find the base cost before VAT.
To find the tariff excluding VAT:
Let [tex]\( \text{Tariff without VAT} = T \)[/tex]
[tex]\( T \times 1.15 = 5.20 \)[/tex]
[tex]\( T = \frac{5.20}{1.15} \)[/tex]
[tex]\( T \approx 4.52 \)[/tex] Rand/kl
Thus, the tariff excluding VAT is approximately R4.52 per kilolitre for water consumption between 10 kl and 20 kl.
### 3. Reasons for Providing Free Water
The municipality supplies the first 6 kl of water to each household at no cost for several reasons, typically:
1. Economic Support:
To assist low-income households by reducing their financial burden, ensuring they have access to water for essential usage.
2. Basic Needs Assurance:
To ensure that all residents can meet their basic water needs without incurring costs they might be unable to afford, promoting public health and hygiene.
### 4. Reason for Different Tariff Rates
The municipality applies different tariff rates for different water consumption intervals to encourage water conservation. Higher tariffs for greater consumption discourage wasteful usage and promote efficient use of water resources. This tiered system ensures that basic needs are met affordably, while excess usage incurs higher charges to stress the importance of conserving a valuable resource.
### 5. Calculating February Water Cost (Including VAT)
For February, Mr. Lavender's water consumption was 30000 litres, which is equivalent to 30 kilolitres (kl).
- The first 6 kl are free.
- The remaining water usage is 24 kl (30 kl - 6 kl), which falls into two tariff groups:
- For the first 10 kl: (10 kl - 6 kl) = 4 kl would be free.
- The remaining 20 kl are charged at R9.20 per kl.
The total cost excluding VAT:
- Water usage beyond 6 kl up to 30 kl = [tex]\( 24 \text{ kl} \times 9.20 \text{ R/kl} \)[/tex]
- Total cost = R220.80 (excluding VAT)
Now, including VAT at 15%:
- Total cost including VAT = [tex]\( 220.80 + (220.80 \times 0.15) \)[/tex]
- Total cost including VAT ≈ R253.92
### 6. May Water Bill Comparison
For May, Mr. Lavender used 15000 litres, which is 15 kilolitres (kl).
- The first 6 kl are free.
- The remaining 9 kl (15 kl - 6 kl) fall into the second tariff group of R5.20 per kl.
The total cost excluding VAT:
- Water usage beyond 6 kl up to 15 kl = [tex]\( 9 \text{ kl} \times 5.20 \text{ R/kl} \)[/tex]
- Total cost = R46.80 (excluding VAT)
Now, including VAT at 15%:
- Total cost including VAT = [tex]\( 46.80 + (46.80 \times 0.15) \)[/tex]
- Total cost including VAT ≈ R53.82
### Conclusion: Comparison of February and May Bills
Mr. Lavender's water bill in May will not be exactly half of his February bill despite using half the amount of water. This is due to the tiered tariff system.
- In February, the consumption exceeded the higher tariff group leading to higher charges.
- In May, the usage fell under a lower tariff group, hence the lower rate was applied. This results in differences due to the tiered pricing structure, rather than a direct proportional relationship based on the amount of water used.
A tariff is a system or schedule of fees or taxes that are applied to particular goods or services. In the context of water usage, it refers to the pricing structure that the municipality charges households for their water consumption based on different usage levels. Essentially, a tariff system determines how much residents pay per unit of water consumed.
### 2. Calculate the Tariffs Excluding VAT for Water Consumption Between 10 kl and 20 kl
To determine the tariffs excluding VAT:
- For water consumption between 10 kilolitres (kl) and 20 kl, the tariff is R5.20 per kilolitre.
- Since there are 15% VAT included in the provided tariff, we can find the base cost before VAT.
To find the tariff excluding VAT:
Let [tex]\( \text{Tariff without VAT} = T \)[/tex]
[tex]\( T \times 1.15 = 5.20 \)[/tex]
[tex]\( T = \frac{5.20}{1.15} \)[/tex]
[tex]\( T \approx 4.52 \)[/tex] Rand/kl
Thus, the tariff excluding VAT is approximately R4.52 per kilolitre for water consumption between 10 kl and 20 kl.
### 3. Reasons for Providing Free Water
The municipality supplies the first 6 kl of water to each household at no cost for several reasons, typically:
1. Economic Support:
To assist low-income households by reducing their financial burden, ensuring they have access to water for essential usage.
2. Basic Needs Assurance:
To ensure that all residents can meet their basic water needs without incurring costs they might be unable to afford, promoting public health and hygiene.
### 4. Reason for Different Tariff Rates
The municipality applies different tariff rates for different water consumption intervals to encourage water conservation. Higher tariffs for greater consumption discourage wasteful usage and promote efficient use of water resources. This tiered system ensures that basic needs are met affordably, while excess usage incurs higher charges to stress the importance of conserving a valuable resource.
### 5. Calculating February Water Cost (Including VAT)
For February, Mr. Lavender's water consumption was 30000 litres, which is equivalent to 30 kilolitres (kl).
- The first 6 kl are free.
- The remaining water usage is 24 kl (30 kl - 6 kl), which falls into two tariff groups:
- For the first 10 kl: (10 kl - 6 kl) = 4 kl would be free.
- The remaining 20 kl are charged at R9.20 per kl.
The total cost excluding VAT:
- Water usage beyond 6 kl up to 30 kl = [tex]\( 24 \text{ kl} \times 9.20 \text{ R/kl} \)[/tex]
- Total cost = R220.80 (excluding VAT)
Now, including VAT at 15%:
- Total cost including VAT = [tex]\( 220.80 + (220.80 \times 0.15) \)[/tex]
- Total cost including VAT ≈ R253.92
### 6. May Water Bill Comparison
For May, Mr. Lavender used 15000 litres, which is 15 kilolitres (kl).
- The first 6 kl are free.
- The remaining 9 kl (15 kl - 6 kl) fall into the second tariff group of R5.20 per kl.
The total cost excluding VAT:
- Water usage beyond 6 kl up to 15 kl = [tex]\( 9 \text{ kl} \times 5.20 \text{ R/kl} \)[/tex]
- Total cost = R46.80 (excluding VAT)
Now, including VAT at 15%:
- Total cost including VAT = [tex]\( 46.80 + (46.80 \times 0.15) \)[/tex]
- Total cost including VAT ≈ R53.82
### Conclusion: Comparison of February and May Bills
Mr. Lavender's water bill in May will not be exactly half of his February bill despite using half the amount of water. This is due to the tiered tariff system.
- In February, the consumption exceeded the higher tariff group leading to higher charges.
- In May, the usage fell under a lower tariff group, hence the lower rate was applied. This results in differences due to the tiered pricing structure, rather than a direct proportional relationship based on the amount of water used.
