Question

The catalogue price of a colour T.V. is Rs.24,000. The shopkeeper gives a discount of 8% on the list price. He gives a further off season discount of 5% on the balance. But sales tax at 10% is charged on the remaining amount. Find:
A. The sales tax customer has to pay.
B. The final price he has to pay for the T.V.
(a) Rs.2,160.60 , Rs.23,112.60
(b) Rs.2,097.60 , Rs.23,073.60
(c) Rs.1,976.60 , Rs.23,243.60
(d) Rs.1,850.60 , Rs.23,513.60

Answer 1

In this question, we need to first look at some of the basic definitions of linear equations. Then we need to calculate how much is 8% in 24,000 and subtract it from the total cost. Now, we need to calculate 5% of the balance and then subtract it from the balance. Then we need to calculate 10% of the remaining amount and add to it.

Complete step-by-step solution -
Let us look at some of the basic definitions.
LINEAR EQUATIONS:
Equation: A statement of equality of two algebraic expressions involving two or more unknown variables is called equation.
Linear Equation: An equation involving the variables in maximum of order 1 is called a linear equation. Graph of a linear equation is a straight line.
Linear equation in one variable is of the form \[ax+b=0\].
Linear equation in two variables is of the form \[ax+by+c=0\].
Equation’s Solution : A particular set of values of the variables, which when substituted for the variables in the equation makes the two sides of the equation equal, is called the solution of the equation.
Now, let us look at the percentage formula.
The value of x% in y can be written as:
\[\dfrac{x}{100}\times y\]
Now, on comparing with the given values we get,
\[x=8,y=24,000\]
Let us assume that the cost after discount as A , cost after season discount as B and cost after sales tax on the remaining amount as C.
\[\begin{align}
  & \Rightarrow A=24000-\dfrac{8}{100}\times 24000 \\
 & \Rightarrow A=24000-\left( 8\times 240 \right) \\
 & \Rightarrow A=24000-1920 \\
 & \therefore A=Rs.22,080 \\
\end{align}\]
Now, again we need to consider the values of x and y as,
\[x=5,y=22,080\]
By using this and simplifying we get,
\[\Rightarrow B=A-\dfrac{x}{100}\times A\]
\[\begin{align}
  & \Rightarrow B=22080-\dfrac{5}{100}\times 22080 \\
 & \Rightarrow B=22080-\left( 5\times 220.8 \right) \\
 & \Rightarrow B=22080-1104 \\
 & \therefore B=Rs.20,976 \\
\end{align}\]
Let us assume that the sales tax will be imposed on the remaining amount as D.
Now, we use \[x=10,y=20,976\].
\[\Rightarrow D=\dfrac{x}{100}\times B\]
\[\begin{align}
  & \Rightarrow D=\dfrac{10}{100}\times 20,976 \\
 & \Rightarrow D=10\times 209.76 \\
 & \therefore D=Rs.2,097.60 \\
\end{align}\]
\[\begin{align}
  & \Rightarrow C=20,976+D \\
 & \Rightarrow C=20,976+2,097.60 \\
 & \therefore C=Rs.23,073.60 \\
\end{align}\]
Hence, the correct option is (b).

Note: It is important to note that the discount of 8% should be calculated from the total amount and then the season off discount should be calculated using the balance after getting the discount and 5% of it should be subtracted. Then we need to add 10% of the remaining amount to the remaining which gives the amount to be paid.
Instead of assigning various variables for it we can directly calculate the amount by first subtracting 8% of the total amount then subtract 5% of that amount and then add 10% to that amount which gives the total amount to be paid.