Sure, let's go through the problem step by step.
### Given Data:
- Water meter readings at the end of each month:
- Baisakh: 6072 units
- Jestha: 6099 units
- Ashad: 6194 units
- Cost for the first 10 units of water: Rs. 100
- Cost per additional unit: Rs. 32
- Drain charge: 50% of the bill amount (excluding rebate)
- Rebate for on-time payment: 3%
### (a) Formula to Calculate the Charge:
To calculate the water bill when the minimum charge, extra units, and the rate for extra units are given, we can use the following formula:
1. Identify the extra units consumed beyond the first 10 units.
2. Calculate the cost for the first 10 units.
3. Calculate the cost for the extra units.
4. Sum these two costs to get the total amount.
5. Calculate the drain charge, which is 50% of the total amount.
6. Add the drain charge to the total amount to get the gross bill.
Mathematically,
[tex]\[
\text{Bill Amount} = \text{Cost for first 10 units} + (\text{Extra units} \times \text{Cost per extra unit})
\][/tex]
[tex]\[
\text{Drain Charge} = \text{Bill Amount} \times 0.50
\][/tex]
[tex]\[
\text{Total Bill} = \text{Bill Amount} + \text{Drain Charge}
\][/tex]
### (b) Calculate the Water Bill for Jestha:
- Units consumed in Jestha = 6099 - 6072 = 27 units
For the month of Jestha:
- Total units consumed: 27 units
- First 10 units cost: Rs. 100
- Extra units: 27 - 10 = 17 units
- Cost of extra units: 17 [tex]\(\times\)[/tex] 32 = Rs. 544
Total without drain charge:
[tex]\[
100 + 544 = Rs. 644
\][/tex]
Drain Charge:
[tex]\[
644 \times 0.50 = Rs. 322
\][/tex]
Total Bill (Jestha):
[tex]\[
644 + 322 = Rs. 966
\][/tex]
Thus, the water bill for Jestha is Rs. 966.
### (c) Calculate the Water Bill for Ashad with Rebate
- Units consumed in Ashad = 6194 - 6099 = 95 units
For the month of Ashad:
- Total units consumed: 95 units
- First 10 units cost: Rs. 100
- Extra units: 95 - 10 = 85 units
- Cost of extra units: 85 [tex]\(\times\)[/tex] 32 = Rs. 2720
Total without drain charge:
[tex]\[
100 + 2720 = Rs. 2820
\][/tex]
Drain Charge:
[tex]\[
2820 \times 0.50 = Rs. 1410
\][/tex]
Total Bill before rebate:
[tex]\[
2820 + 1410 = Rs. 4230
\][/tex]
Rebate:
[tex]\[
4230 \times 0.03 = Rs. 126.90
\][/tex]
Total Bill after rebate:
[tex]\[
4230 - 126.90 = Rs. 4103.10
\][/tex]
Thus, the water bill for Ashad with rebate is Rs. 4103.10.
### Determine the More Economical Month
Comparing the water bills:
- Jestha: Rs. 966
- Ashad (with rebate): Rs. 4103.10
The month of Jestha is more economical. The reason is that the bill for Jestha is substantially lower at Rs. 966 compared to the bill for Ashad, even after accounting for the rebate, which amounts to Rs. 4103.10. This is because the number of units consumed in Jestha was significantly lower than in Ashad.
