Question

The cost of furniture inclusive of VAT is Rs. 7150. If the rate of VAT is 10%, find the original cost of the furniture.
(A) Rs. 5000
(B) Rs. 3000
(C) Rs. 6500
(D) Rs. 2000

Answer 1

Hint: Assume the actual cost price of the furniture be Rs. x. We know that the VAT is imposed on the actual cost price of the furniture to get the cost of the furniture. So, we can say that, the cost of the furniture is equal to the summation of the VAT and actual price of the furniture. The rate is 10% and the cost of the furniture is Rs. 7150. Now, solve it further and get the value of x.

Complete step by step solution:
According to the question, it is given that the cost of the furniture inclusive of VAT is equal to Rs. 7150. It is also given that the rate of VAT is equal to 10% and we are asked to get the cost of the furniture.
The cost of the furniture inclusive of VAT = Rs. 7150 …………………………..(1)
The rate of VAT = 10% ……………………………(2)
Now, let us assume the actual cost price of the furniture will be Rs. x.
Since the VAT is getting imposed on the actual cost price of the furniture, 10% of the actual cost price is added to the actual cost price to get the cost of the furniture inclusive of VAT.
From equation (2), we have the rate of VAT which is getting imposed on the actual cost price of the furniture to obtain the cost of the furniture.
So, we can say that, the cost of the furniture is equal to the summation of the VAT and actual price of the furniture
The cost of furniture inclusive of VAT =Rs. (x + 10% of x) ………………………(3)
From equation (1), we have the cost price of the furniture including VAT.
Now, comparing equation (1) and equation (3), we get
\[\begin{align}
  & 7150=x+10\%\,of\,x \\
 & \Rightarrow 7150=x+\dfrac{10}{100}x \\
 & \Rightarrow 7150=x+\dfrac{x}{10} \\
 & \Rightarrow 7150=\dfrac{10x+x}{10} \\
 & \Rightarrow 7150=\dfrac{11x}{10} \\
\end{align}\]
\[\begin{align}
  & \Rightarrow \dfrac{7150\times 10}{11}=x \\
 & \Rightarrow 650\times 10=x \\
 & \Rightarrow 6500=x \\
\end{align}\]
Therefore, the actual cost of the furniture is Rs. 6500.
Hence, option (C) is the correct one.

Note: In this question, one might think that VAT is included in the cost of furniture. So, to get the actual cost of the furniture one might subtract 10% of Rs. 7150 from Rs. 7150.
\[\begin{align}
  & 7150-10\%\,of\,7150 \\
 & =7150-\dfrac{10}{100}\times 7150 \\
 & =7150-715 \\
 & =6435 \\
\end{align}\]
This is wrong because the VAT is getting imposed on the actual price of the furniture. Hence, to get the actual cost of the furniture the rate of VAT should not be subtracted from the given cost of the furniture.