Answer :
Let's go through each part of the question step by step.
### (i) How many units of water is consumed in Aswin month?
To find the number of units consumed, we subtract the initial reading from the final reading:
- Initial Reading on 1 Aswin: 2020 units
- Final Reading on 1 Kartik: 2050 units
[tex]\[ \text{Units Consumed} = 2050 - 2020 = 30 \text{ units} \][/tex]
### (ii) How much sewerage service charge should he pay?
First, we calculate the water consumption charge. According to KUKL:
- Minimum charge for up to 27 units: Rs 1,910
- Additional charge per unit beyond 27 units: Rs 71
Since Mr. Maharjan consumed 30 units:
- Units above the 27-unit minimum: [tex]\( 30 - 27 = 3 \text{ units} \)[/tex]
- Additional charge for the 3 units: [tex]\( 3 \times 71 = 213 \text{ Rs} \)[/tex]
Total water consumption charge:
[tex]\[ \text{Total water charge} = 1910 + 213 = 2123 \text{ Rs} \][/tex]
The sewerage service charge is 50% of the total water charge:
[tex]\[ \text{Sewerage Service Charge} = 0.5 \times 2123 = 1061.5 \text{ Rs} \][/tex]
### (iii) Find the total bill including [tex]$50 \%$[/tex] sewerage service charge.
The total bill includes both the water charge and the sewerage service charge:
[tex]\[ \text{Total Bill} = \text{Total Water Charge} + \text{Sewerage Service Charge} \][/tex]
[tex]\[ \text{Total Bill} = 2123 + 1061.5 = 3184.5 \text{ Rs} \][/tex]
### (iv) If he paid only Rs 3,717 for the consumption of water in Falgun, how many units of water was consumed in the month of Falgun?
Given:
- Total payment in Falgun (including sewerage service charge): Rs 3,717
- Since the total payment includes a 50% sewerage service charge, we can represent it as:
[tex]\[ \text{Total Payment} = 1.5 \times \text{Total Water Charge} \][/tex]
To find the total water charge:
[tex]\[ \text{Total Water Charge} = \frac{3717}{1.5} = 2478 \text{ Rs} \][/tex]
Now, we use the total water charge to find the number of units consumed:
- If the total water charge is less than or equal to Rs 1,910, the units consumed would be 27 or less. In this case, it's more than Rs 1,910.
Let's find the additional units consumed:
- Additional cost: [tex]\( 2478 - 1910 = 568 \text{ Rs} \)[/tex]
- Additional units consumed: [tex]\( \frac{568}{71} = 8 \text{ units} \)[/tex]
Total units consumed in Falgun:
[tex]\[ \text{Units Consumed in Falgun} = 27 + 8 = 35 \text{ units} \][/tex]
In summary:
(i) 30 units of water were consumed in Aswin month.
(ii) The sewerage service charge is Rs 1061.5.
(iii) The total bill including the sewerage service charge is Rs 3184.5.
(iv) In the month of Falgun, 35 units of water were consumed.
### (i) How many units of water is consumed in Aswin month?
To find the number of units consumed, we subtract the initial reading from the final reading:
- Initial Reading on 1 Aswin: 2020 units
- Final Reading on 1 Kartik: 2050 units
[tex]\[ \text{Units Consumed} = 2050 - 2020 = 30 \text{ units} \][/tex]
### (ii) How much sewerage service charge should he pay?
First, we calculate the water consumption charge. According to KUKL:
- Minimum charge for up to 27 units: Rs 1,910
- Additional charge per unit beyond 27 units: Rs 71
Since Mr. Maharjan consumed 30 units:
- Units above the 27-unit minimum: [tex]\( 30 - 27 = 3 \text{ units} \)[/tex]
- Additional charge for the 3 units: [tex]\( 3 \times 71 = 213 \text{ Rs} \)[/tex]
Total water consumption charge:
[tex]\[ \text{Total water charge} = 1910 + 213 = 2123 \text{ Rs} \][/tex]
The sewerage service charge is 50% of the total water charge:
[tex]\[ \text{Sewerage Service Charge} = 0.5 \times 2123 = 1061.5 \text{ Rs} \][/tex]
### (iii) Find the total bill including [tex]$50 \%$[/tex] sewerage service charge.
The total bill includes both the water charge and the sewerage service charge:
[tex]\[ \text{Total Bill} = \text{Total Water Charge} + \text{Sewerage Service Charge} \][/tex]
[tex]\[ \text{Total Bill} = 2123 + 1061.5 = 3184.5 \text{ Rs} \][/tex]
### (iv) If he paid only Rs 3,717 for the consumption of water in Falgun, how many units of water was consumed in the month of Falgun?
Given:
- Total payment in Falgun (including sewerage service charge): Rs 3,717
- Since the total payment includes a 50% sewerage service charge, we can represent it as:
[tex]\[ \text{Total Payment} = 1.5 \times \text{Total Water Charge} \][/tex]
To find the total water charge:
[tex]\[ \text{Total Water Charge} = \frac{3717}{1.5} = 2478 \text{ Rs} \][/tex]
Now, we use the total water charge to find the number of units consumed:
- If the total water charge is less than or equal to Rs 1,910, the units consumed would be 27 or less. In this case, it's more than Rs 1,910.
Let's find the additional units consumed:
- Additional cost: [tex]\( 2478 - 1910 = 568 \text{ Rs} \)[/tex]
- Additional units consumed: [tex]\( \frac{568}{71} = 8 \text{ units} \)[/tex]
Total units consumed in Falgun:
[tex]\[ \text{Units Consumed in Falgun} = 27 + 8 = 35 \text{ units} \][/tex]
In summary:
(i) 30 units of water were consumed in Aswin month.
(ii) The sewerage service charge is Rs 1061.5.
(iii) The total bill including the sewerage service charge is Rs 3184.5.
(iv) In the month of Falgun, 35 units of water were consumed.
