Question

If VAT is included in the price, find the original price of each of the following:

S. No.	Item	VAT	Bill Amount (in Rs)
1.	Diamond	$1\%$	Rs. 10, 100
2.	Pressure Cooker	$5\%$	Rs. 2940
3.	Face powder	$14.5\%$	Rs. 229

Answer 1

Hint: Let us assume that the original price of diamond, pressure cooker and face powder is “d, p and f” respectively. Now, take $1\%$ of the original price of the diamond and add to the original price of the diamond and equate it to 10, 100. Solve this equation and get the value of original price of diamond “d”. Similarly, you can find the original price for pressure cooker and face powder also.

Complete step by step answer:
Let us assume that the original price of diamond, pressure cooker and face powder is “d, p and f” respectively.
First of all we are going to find the original price of diamond by taking $1\%$ of the original price of the diamond and add to the original price of the diamond and equate it to 10, 100.
Taking $1\%$ of the original price of the diamond by multiplying d by 1 and then dividing by 100 we get,
$d\left( \dfrac{1}{100} \right)$
Now, adding the original price “d” in the above expression we get,
$d+\dfrac{d}{100}$
Taking d as common in the above expression we get,
$d\left( 1+\dfrac{1}{100} \right)$
Equating the above expression to 10, 100 we get,
$\begin{align}
  & d\left( 1+\dfrac{1}{100} \right)=10100 \\
 & \Rightarrow d\left( \dfrac{100+1}{100} \right)=10100 \\
 & \Rightarrow d=\dfrac{10100\left( 100 \right)}{101} \\
\end{align}$
101 will be cancelled out from the numerator and the denominator we get,
$d=10000$
Hence, the original price of diamond is Rs. 10, 000.
Now, finding the original price of pressure cooker in the same way as we have found the price of diamond we get,
Taking $5\%$ of the original price of the pressure cooker by multiplying “p” by 5 and then dividing by 100 we get,
$\begin{align}
  & p\left( \dfrac{5}{100} \right) \\
 & =\dfrac{5p}{100} \\
\end{align}$
Adding “p” to the above expression we get,
$p+\dfrac{5p}{100}$
Taking “p” as common in the above solution we get,
$\begin{align}
  & p\left( 1+\dfrac{5}{100} \right) \\
 & =p\left( \dfrac{100+5}{100} \right) \\
 & =p\left( \dfrac{105}{100} \right) \\
\end{align}$
Equating the above expression to 2940 we get,
$p\left( \dfrac{105}{100} \right)=2940$
$\begin{align}
  & \Rightarrow p=\dfrac{2940\left( 100 \right)}{105} \\
 & \Rightarrow p=2800 \\
\end{align}$
Hence, we have got the original price of the pressure cooker as Rs 2800.
Now, we are going to find the original price of face powder as follows:
Taking $14.5\%$ of the original price of the face powder by multiplying “f” by 14.5 and then dividing by 100 we get,
$\begin{align}
  & f\left( \dfrac{14.5}{100} \right) \\
 & =\dfrac{14.5f}{100} \\
\end{align}$
Adding “f” to the above expression we get,
$f+\dfrac{14.5f}{100}$
Taking “f” as common in the above solution we get,
$\begin{align}
  & f\left( 1+\dfrac{14.5}{100} \right) \\
 & =f\left( \dfrac{100+14.5}{100} \right) \\
 & =f\left( \dfrac{114.5}{100} \right) \\
\end{align}$
Equating the above expression to 229 we get,
$f\left( \dfrac{114.5}{100} \right)=229$
$\begin{align}
  & \Rightarrow f=\dfrac{229\left( 100 \right)}{114.5} \\
 & \Rightarrow f=200 \\
\end{align}$

Hence, we have got the original price of the face powder as Rs 200.

Note: The possibility of making a mistake in this problem is instead of putting VAT on the original price, you might do the calculation by putting VAT on the billing amount. To avoid this problem, remember that VAT is the Value Added Tax so the billing amount includes the VAT so we have to take VAT on the original price not on the billing amount.
You can check whether the original price that you are getting is correct or not by taking VAT on that original price and then add the original price to it and see whether the billing amount is equal to the given billing amount or not.
For instance, the original price of diamond that we are getting is Rs. 10, 000. Now, taking $1%$ of 10000 we get,
$\begin{align}
  & 10000\left( \dfrac{1}{100} \right) \\
 & =100 \\
\end{align}$
Now, adding 10000 to 100 we get,
$\begin{align}
  & 10000+100 \\
 & =10100 \\
\end{align}$
Hence, the billing amount that we are getting is matching with the given billing amount. Hence, the original price that we have calculated is correct. Similarly, you can check other items too.