Question

A colour TV is available for Rs 13,440 inclusive of sales tax. If the original cost of TV is Rs 12,000, then the rate of sales tax is:
A) \[10\% \]
B) \[12\% \]
C) \[13\% \]
D) \[14\% \]

Answer 1

Hint:
Here, we will find the cost of the TV including VAT and then we will add the original price with the \[x\% \] of the original cost. Then we will simplify the obtained equation to find the required value.

Complete step by step solution:
We are given that a colour TV is available for Rs 13,440 inclusive of sales tax and the original cost of TV is Rs 12,000.
Let us assume the rate of VAT be \[x\% \].
First, we will find the cost of the TV including VAT, we get
\[ \Rightarrow 13,440\]
We will now add the original price with the \[x\% \] of the original cost, we get
\[
   \Rightarrow {\text{Cost of the TV}} = x\% \times 12000 + 12000 \\
   \Rightarrow {\text{Cost of the TV}} = \dfrac{x}{{100}} \times 12000 + 12000 \\
   \Rightarrow {\text{Cost of the TV}} = 120x + 12000 \\
 \]
Substituting the value of the cost price of the TV in the above equation, we get
\[ \Rightarrow 13440 = 12x + 12000\]
Subtracting the above equation by 12000 on both sides, we get
\[
   \Rightarrow 13440 - 12000 = 12x + 12000 - 12000 \\
   \Rightarrow 1440 = 12x \\
 \]
Dividing the above equation by 14 into both sides, we get
\[
   \Rightarrow \dfrac{{1440}}{{12}} = \dfrac{{12x}}{{12}} \\
   \Rightarrow 120 = x \\
   \Rightarrow x = 120 \\
 \]
Therefore, the rate of VAT on the colour TV is \[12\% \].

Hence, the option is B will be correct.

Note:
In this question, the student should find out the cost of the TV by comparing between the selling price and the costing price. In solving these types of questions, you should be familiar with the cost price, selling price and VAT. Then use the given conditions and values given in the question, to find the cost.