The problem involves calculating an electricity bill composed of a fixed charge and a variable charge based on electricity units consumed. We need to determine the fixed and variable rates from the given data and then calculate the bill for a specific consumption.
Formulating Equations for Electricity Bill
Let F represent the fixed charge (in ₹) and V represent the variable charge per unit (in ₹/unit). The total bill (B) is calculated using the formula: B = F + V × U, where U is the number of units consumed.
From the given information:
- Month 1: 540 units consumed, Bill = ₹1,800. This gives the equation:
$1800 = F + 540V$ (Equation 1) - Month 2: 620 units consumed, Bill = ₹2,040. This gives the equation:
$2040 = F + 620V$ (Equation 2)
Calculating Variable Charge per Unit (V)
To find the variable charge per unit (V), we subtract Equation 1 from Equation 2:
$(2040 - 1800) = (F + 620V) - (F + 540V)$
$240 = 620V - 540V$
$240 = 80V$
Now, solve for V:
$V = \frac{240}{80}$$V = 3$
So, the variable charge is ₹3 per unit.
Calculating Fixed Charge (F)
Substitute the value of V (₹3) back into Equation 1 to find the fixed charge (F):
$1800 = F + 540 \times 3$$1800 = F + 1620$
$F = 1800 - 1620$
$F = 180$
The fixed charge is ₹180.
Calculating Bill for 500 Units
Now, calculate the bill for a month when 500 units are consumed using the determined values of F and V:
$B = F + V \times U$$B = 180 + 3 \times 500$
$B = 180 + 1500$
$B = 1680$
Therefore, the bill for 500 units consumed will be ₹1,680.
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