Question

Find the original price of a washing machine, if the price of the washing machine including a tax of 8 % is Rs. 8000.

Answer 1

Hint: First of all, take the original price of the washing machine as x. Now, use (the original price of the washing machine) + (8 % of the original price of the washing machine) = 8000. From this, find the value of x to get the required answer.

Complete step-by-step answer:

In this question, we have to find the original price of a washing machine, if the price of the washing machine including a tax of 8 % is Rs. 8000. Before proceeding with the question, let us see what tax or sales tax is. A tax is basically the amount that is added to the price of the particular goods and services. It is usually given as a percentage of the purchase price. It can have various examples like GST, VAT, etc.
Suppose, the original price of an entity is x. Now, x % tax is added to it. So, its price becomes x + [n % of x] \[=x+\dfrac{nx}{100}=x\left[ 1+\dfrac{n}{100} \right]\].
Now, let us consider our question. We are given that the price of the washing machine including a tax of 8 % is Rs. 8000. Let us take the original price of the washing machine as x. So, by the given information, we get,
(Original Price of the Washing Machine) + (8 % of Original Price of Washing Machine) = Actual Price.
x + (8 % of x) = Rs. 8000
\[x+\dfrac{8x}{100}=8000\]
\[\dfrac{100x+8x}{100}=8000\]
\[\dfrac{108x}{100}=8000\]
\[x=8000\times \dfrac{100}{108}\]
x = Rs. 7407.41
So, we get the original price of the washing machine as Rs. 7407.41

Note: In this question n, many students make this mistake of finding the original price by using [8000 + (8 % of 8000)] which is wrong because the total price is 8000 and not the original price. Also, students must remember that the original price that is the price of an entity without taxes is always less than with taxes. So, from this, we can say that the original price of the washing machine would be at least less than Rs. 8000.