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. 1800. In another month 620 units are consumed, the bill is Rs.2040. In yet another month 500 units. Are consumed then, the bill for that month would be
${\text{A}}{\text{.}}$Rs. 1560
${\text{B}}{\text{.}}$Rs. 1680
${\text{C}}{\text{.}}$Rs. 1840
${\text{D}}{\text{.}}$Rs. 1950

Answer 1

Hint:In this question first we have to make an equation of bill using a partly fixed amount and a varying amount. After that we have to find the value of the fixed amount and cost of one unit. And finally put these two in the equation of bill to get bill of month in which units consumed are 500.

Complete step-by-step answer:
The electricity bill is a summation of the partly fixed amount and the varying amount which depends on the number of units of electricity consumed.
Bill = fixed amount + number of units in that month$ \times $cost of one unit eq.1
Let the fixed amount be Rs. $x$and the cost of each unit be Rs.$y$.
Now, when in a certain month 540 units are consumed, the bill is Rs. 1800.i.e.,
$ \Rightarrow 540y + x = 1800{\text{ eq}}{\text{.2}}$
And, when in another month 620 units are consumed, the bill is Rs. 2040.i.e.,
$ \Rightarrow 620y + x = 2040{\text{ eq}}{\text{.3}}$
Now, subtract the eq.2 from eq.3 we get
$
   \Rightarrow 80y = 240 \\
   \Rightarrow y = 3{\text{ eq}}{\text{.3}} \\
 $
Therefore, the cost of each unit is Rs.3
Now, put $y = 3$in eq.1 we get
$
   \Rightarrow 540y + x = 1800 \\
   \Rightarrow 540 \times 3 + x = 1800 \\
   \Rightarrow x = 1800 - 1620 \\
   \Rightarrow x = 180 \\
$
Therefore, the partly fixed amount is Rs. 180.
Now, the bill for another month in which the number of units consumed are 500.
Then,
$
   \Rightarrow Rs.(180{\text{ }} + {\text{ 500}} \times {\text{3) \{ }}\because x = Rs.180;{\text{ y = Rs}}{\text{.3\} }} \\
   \Rightarrow Rs.1680 \\
 $
Therefore, the bill for the month in which the number of units consumed are 500 is Rs. 1680.
Hence, option B is correct.

Note:Whenever you get this type of question the key concept to solve is to make equation because after making equations from given things, it is bit is to get answer as in this question we make equation of bill (Bill= fixed amount + number of units in that month$ \times $cost of one unit). And then find the unknown terms in formula.