Answer
414.3k+ views
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.
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.
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