Question

A mobile company charges a fixed amount as a monthly rental which includes 100 minutes free per month and charges a fixed amount for every additional minute. Aarav paid Rs. 433 for 370 minutes and Ashish paid Rs. 398 for 300 minutes. Find the bill amount under the same plan, if Ushma uses for 400 minutes.

Answer 1

Hint: Let us assume that charges for 100 minutes is Rs. x and charges for every additional minute is Rs. y. So, we can say that bill paid by Aarav in terms of x and y is $x+(370-100)y=433$.
Similarly, bill paid by Ashish can be written as $x+\left( 300-100 \right)y=398$
So, we have a set of linear equations with two variables. Solve the above equations and get the values of variables x and y.
Now, we can also write an equation for the bill paid by Ushma in terms of x and y as:
$x+(400-100)y=?$
Substitute the values of x and y in the equation and the amount of bill paid by Ushma.

Complete step-by-step solution:
Since, it is given in the question that bill paid by Aarav is Rs. 433 and bill paid by Ashish is Rs. 398, so we can form two equations with two variables as:
$\begin{align}
  & x+270y=433......(1) \\
 & x+200y=398......(2) \\
\end{align}$
Subtract equation (2) from equation (1), we get:
$\begin{align}
  & \Rightarrow 70y=35 \\
 & \Rightarrow y=0.5......(3) \\
\end{align}$
Hence charges for each additional minute is Rs. 0.5.
Put y = 0.5 in equation (1), we get:
$\begin{align}
  & \Rightarrow x+270\left( 0.5 \right)=433 \\
 & \Rightarrow x=433-135 \\
 & \Rightarrow x=298......(4) \\
\end{align}$
So, the charges for 100 minutes are Rs. 298.
Now, we need to calculate the bill paid by Ushma for 400 minutes, so splitting bill into 100+300 minutes we get an equation as:
$\begin{align}
  & =x+300y \\
 & =298+300\left( 0.5 \right) \\
 & =448 \\
\end{align}$
Hence the bill paid by Ushma is Rs. 448

Note: Since it is mentioned that the plan includes free 100 minutes, don’t get confused that the charges for 100 minutes are Rs. 0. Instead, assume a fixed amount for 100 minutes and a variable amount for additional minutes. Here the charge for 100 minutes is to be constant which we got as 298 Rs.