Question

Sunil bought a TV for \[Rs22000\] including a GST of \[10\% \], Find the price of the TV before GST was added.

Answer 1

Hint: Here, selling price is the sum of cost price and the GST of \[10\% \]

The selling price is given. So we will take a random variable as the cost price then calculate the selling price on that, then equating these two selling prices we will get the price of the TV before adding the GST.

 \[SP = CP + CP \times GST\]

Complete step by step answer:

It is given that, the Sunil bought a TV for\[Rs22000\] including a GST of \[10\% \]

Let us consider that Sunil bought the TV without GST at Rs.$x$.

The GST amount is given as \[10\% \] of $x$.

That is by using the percentage formula we get,

\[\Rightarrow x \times \dfrac{{10}}{{100}}\] \[ = \dfrac{x}{{10}}\]

Let us now add the percentage of the amount and the amount of TV.

Thus after adding GST the amount to the TV amount and on solving the equation we get,

\[\Rightarrow x + \dfrac{x}{{10}} = \dfrac{{10x + x}}{{10}} = \dfrac{{11x}}{{10}}\] … (1)

It is given that Sunil bought the TV for \[Rs.22000\] including a GST of \[10\% \].

Let us now equate the amount Sunil bought the TV and equation (1).

By equating both the terms we get,

\[\Rightarrow \dfrac{{11x}}{{10}} = 22000\]

Let us solve the above equation to get the value of $x$, we get,

\[\Rightarrow x = \dfrac{{22000 \times 10}}{{11}}\]

And on further solving we get the value of $x$,

\[\Rightarrow x{\rm{ }} = Rs.{\rm{ }}20000\]

$\therefore$ The price of the TV before GST was added is Rs.20000.

Note:

The percentage of $x$ is denoted by %x and it is defined by \[x% = \dfrac{x}{{100}}\]. We should be careful while finding the addition of percentage and the amount of the TV. As it is an important step while finding the value of TV.