Question

The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Rs. 1,800. In another month 620 units are consumed and the bill is Rs. 2,040. In yet another month 500 units are consumed. The bill for that month would be

• A. Rs. 1,560
• B. Rs. 1,680
• C. Rs. 1,840
• D. Rs. 1,950

Hint:

For problems with a fixed and variable component, form two equations based on given values and solve for constants.

Answer 1

The Correct Option is B

Let the fixed charge be \( F \) and the variable charge per unit be \( V \).
From the given data: \[ F + 540V = 1800 \] \[ F + 620V = 2040 \] Subtracting the first equation from the second: \[ (620V + F) - (540V + F) = 2040 - 1800 \] \[ 80V = 240 \] \[ V = 3 \] Substituting \( V = 3 \) in the first equation: \[ F + 540(C) = 1800 \] \[ F + 1620 = 1800 \] \[ F = 180 \] For 500 units consumed: \[ F + 500V = 180 + 500(C) \] \[ = 180 + 1500 = 1680 \] Thus, the bill for that month is Rs. 1,680.