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For the electricity rate, the cost upto 50 units is Rs. 500 and the rate of extra unit is Rs. 15 for a room rental. (a) How many electricity is consumed for 1 unit? (b) How many additional units did the tenant consume if their monthly bill was Rs. 621.50 ? (c) Calculate the bill for the next month if the tenant uses 105 units of electricity. (d) Compare the bills for two successive months'.

Ask by Mcfarlane Coleman. in Nepal
Feb 17,2025

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Answer

(a) The cost per unit for the first 50 units is Rs. 10. (b) The tenant consumed approximately 8 additional units. (c) The bill for the next month with 105 units is Rs. 1325. (d) The bill increased by Rs. 703.50 from the previous month.

Solution

Let's break down the problem step by step. ### Known Conditions: 1. Cost for the first 50 units: Rs. 500 2. Rate for additional units beyond 50: Rs. 15 per unit 3. Monthly bill for the tenant: Rs. 621.50 ### (a) How many electricity is consumed for 1 unit? The cost for the first 50 units is Rs. 500. Therefore, the cost per unit for the first 50 units can be calculated as follows: \[ \text{Cost per unit} = \frac{\text{Total cost for first 50 units}}{\text{Number of units}} = \frac{500}{50} \] Let's calculate this. ### (b) How many additional units did the tenant consume if their monthly bill was Rs. 621.50? The total bill is Rs. 621.50. The first 50 units cost Rs. 500, so we can find the cost of the additional units: \[ \text{Cost of additional units} = \text{Total bill} - \text{Cost for first 50 units} = 621.50 - 500 \] Now, we can find the number of additional units consumed: \[ \text{Number of additional units} = \frac{\text{Cost of additional units}}{\text{Rate per additional unit}} = \frac{\text{Cost of additional units}}{15} \] ### (c) Calculate the bill for the next month if the tenant uses 105 units of electricity. For 105 units, the first 50 units cost Rs. 500. The additional units are: \[ \text{Additional units} = 105 - 50 = 55 \] The cost for these additional units is: \[ \text{Cost for additional units} = 55 \times 15 \] The total bill for the next month will be: \[ \text{Total bill} = \text{Cost for first 50 units} + \text{Cost for additional units} \] ### (d) Compare the bills for two successive months. We will compare the bill from part (b) and the bill from part (c). Now, let's perform the calculations for parts (a), (b), and (c). Calculate the value by following steps: - step0: Calculate: \(621.5-500\) - step1: Subtract the numbers: \(121.5\) Calculate or simplify the expression \( 500 + (55 * 15) \). Calculate the value by following steps: - step0: Calculate: \(500+\left(55\times 15\right)\) - step1: Multiply the numbers: \(500+825\) - step2: Add the numbers: \(1325\) Calculate or simplify the expression \( 55 * 15 \). Calculate the value by following steps: - step0: Calculate: \(55\times 15\) - step1: Multiply the numbers: \(825\) Calculate or simplify the expression \( (621.50 - 500)/15 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(621.5-500\right)}{15}\) - step1: Remove the parentheses: \(\frac{621.5-500}{15}\) - step2: Subtract the numbers: \(\frac{121.5}{15}\) - step3: Convert the expressions: \(\frac{\frac{243}{2}}{15}\) - step4: Multiply by the reciprocal: \(\frac{243}{2}\times \frac{1}{15}\) - step5: Reduce the numbers: \(\frac{81}{2}\times \frac{1}{5}\) - step6: Multiply the fractions: \(\frac{81}{2\times 5}\) - step7: Multiply: \(\frac{81}{10}\) Calculate or simplify the expression \( 500/50 \). Calculate the value by following steps: - step0: Calculate: \(\frac{500}{50}\) - step1: Reduce the numbers: \(\frac{10}{1}\) - step2: Calculate: \(10\) ### (a) How many electricity is consumed for 1 unit? The cost per unit for the first 50 units is: \[ \text{Cost per unit} = 10 \text{ Rs.} \] ### (b) How many additional units did the tenant consume if their monthly bill was Rs. 621.50? The cost of additional units is: \[ \text{Cost of additional units} = 621.50 - 500 = 121.5 \text{ Rs.} \] The number of additional units consumed is: \[ \text{Number of additional units} = \frac{121.5}{15} = 8.1 \text{ units} \] Since we typically consider whole units, the tenant consumed approximately 8 additional units. ### (c) Calculate the bill for the next month if the tenant uses 105 units of electricity. The cost for the additional 55 units (105 - 50) is: \[ \text{Cost for additional units} = 55 \times 15 = 825 \text{ Rs.} \] The total bill for the next month is: \[ \text{Total bill} = 500 + 825 = 1325 \text{ Rs.} \] ### (d) Compare the bills for two successive months. - **First month bill**: Rs. 621.50 - **Second month bill**: Rs. 1325 ### Comparison: The bill increased from Rs. 621.50 to Rs. 1325, which is an increase of: \[ 1325 - 621.50 = 703.50 \text{ Rs.} \] ### Summary: - **Cost per unit**: Rs. 10 - **Additional units consumed**: Approximately 8 units - **Next month's bill**: Rs. 1325 - **Increase in bill**: Rs. 703.50 This concludes the calculations and comparisons for the electricity bills.

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The Deep Dive

(a) The cost for the first 50 units is Rs. 500, so the cost per unit for these initial 50 units can be calculated by dividing Rs. 500 by 50. This gives us Rs. 10 per unit for the first 50 units of electricity consumed. (b) The tenant's monthly bill is Rs. 621.50. Since the first 50 units cost Rs. 500, the remaining bill amount is Rs. 621.50 - Rs. 500 = Rs. 121.50. The additional units consumed can now be found by dividing Rs. 121.50 by Rs. 15, which equals 8.1. Since you can't consume a fraction of a unit, the tenant consumed 8 additional units. (c) If the tenant uses 105 units, the first 50 units will still cost Rs. 500. The additional consumption is 105 - 50 = 55 units, leading to a charge of 55 x Rs. 15 = Rs. 825 for those extra units. The total bill for the next month would thus be Rs. 500 + Rs. 825 = Rs. 1325. (d) Comparing the two bills, the first month's bill was Rs. 621.50 while the second month's bill came to Rs. 1325. This reflects a significant increase of Rs. 703.50, emphasizing how the added consumption of electricity impacts overall costs!

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