Question

The price of a cooker is \[£720\] including VAT at \[20\% \] .What is the price without the VAT?

Answer 1

Hint: In order to solve this question, we should know that the price given in the question is known as bill amount, which is inclusive of VAT and the price, we need to find out is known as the original price. To solve this, we will assume that the price of cooker be \[£x\] .After that we will take \[20\% \] of the price of the cooker and add to the price of the cooker and equate it to \[720\] .Solve this equation and we will get the price of the cooker without VAT.

Complete step-by-step answer:
Let us assume that the price or we can say original price of the cooker i.e., without VAT to be \[x\]
Now we are going to find the price of the cooker by taking \[20\% \] of the price of the cooker and add to the price of the cooker and equate it to \[720\] .
So first we have to take \[20\% \] of the price of the cooker.
which means multiply \[x\] by \[20\] and then divide it by \[100\] we get
\[x\left( {\dfrac{{20}}{{100}}} \right) - - - \left( 1 \right)\]
Now adding price \[x\] in the equation \[\left( 1 \right)\] , we get
\[x + x\left( {\dfrac{{20}}{{100}}} \right)\]
\[ \Rightarrow x + \left( {\dfrac{{20x}}{{100}}} \right) - - - \left( 2 \right)\]
Taking \[x\] common from the equation \[\left( 2 \right)\] , we get
\[x\left( {1 + \dfrac{{20}}{{100}}} \right) - - - \left( 3 \right)\]
Now equating the equation \[\left( 3 \right)\] with \[720\] we get
\[x\left( {1 + \dfrac{{20}}{{100}}} \right) = 720\]
\[ \Rightarrow x\left( {\dfrac{{100 + 20}}{{100}}} \right) = 720\]
On simplifying it we get
\[x\left( {\dfrac{{120}}{{100}}} \right) = 720\]
now multiply both sides by \[100\] we get
\[x\left( {120} \right) = 720 \times 100\]
\[ \Rightarrow x = \dfrac{{720 \times 100}}{{120}}\]
On dividing, we get
\[x = 600\]
So, the correct answer is “s \[£ 6000\]”.

Note: The possibility of making a mistake in this type of question is that instead of taking VAT on the original price, we might do the calculation by taking VAT on the billing price (i.e., given price). To avoid such problems, remember that VAT is the Value Added Tax, so the billing price includes VAT. So, we have to take VAT on the original price, not on the billing price.
Also, we can check whether the price that we are getting is correct or not by taking VAT on that price and then adding the price to it. For instance, the price of the cooker that we are getting is \[£ 600\] Now taking \[20\% \] of \[600\] we get
\[\dfrac{{20}}{{100}} \times 600 = 120\]
Now on adding \[600\] to \[120\] we get
\[600 + 120 = 720\]
Hence, the price that we are getting is correct as it is matching the given price.