Question

The sales price of an article including the sales tax is Rs.616. The rate of sales tax is 10%. If the shopkeeper made a profit of 12%, then the cost price of the article is
(a) Rs.500
(b) Rs.515
(c) Rs.550
(d) Rs.600

Answer 1

Hint: In this question, let us assume the cost price of the article as x. Then using the profit formula given by \[SP=\dfrac{100+x}{100}\times CP\]we can get the selling price in terms of cost price. Now, on adding 10% sales tax on this selling price we get the final selling price which is Rs.616. Now, on further simplification we get the value of x.

Complete step-by-step answer:
Now, from the given conditions in the question the final selling price of the article is Rs.616
Now, let us assume the cost price of the article as Rs. x
As we already know that from the profit formula that if profit is x%, then
\[SP=\dfrac{100+x}{100}\times CP\]
Now, given in the question that profit is 12%
Now, on substituting the respective values in the above formula we get,
\[\Rightarrow SP=\dfrac{100+12}{100}\times x\]
Now, on further simplification we get,
\[\Rightarrow SP=\dfrac{112x}{100}\]
Now, on adding a sales tax on this selling price we get the price at which the article is sold
Given that sales tax is 10%
\[\Rightarrow \dfrac{112x}{100}+\dfrac{112x}{100}\times \dfrac{10}{100}\]
Now, already given in the question that selling price of article with sales tax is Rs.616
Now, on equating the above expression with Rs.616 we get,
\[\Rightarrow \dfrac{112x}{100}+\dfrac{112x}{100}\times \dfrac{10}{100}=616\]
Now, this can also be written as
\[\Rightarrow \dfrac{112x}{100}+\dfrac{112x}{1000}=616\]
Now, on further simplification we get,
\[\Rightarrow \dfrac{1120x+112x}{1000}=616\]
Now, this can be further written in the simplified form as
\[\Rightarrow \dfrac{1232x}{1000}=616\]
Now, on rearranging the terms in the above equation we get,
\[\Rightarrow x=\dfrac{616\times 1000}{1232}\]
Now, on simplifying it further we get,
\[\therefore x=500\]
Thus, the cost price of the article is Rs.500
Hence, the correct option is (a).

Note:Instead of finding the selling price from profit and adding sales tax to it we can also solve this by assuming sales price as x and on profit equating it to Rs.616. Then finding the selling price if CP is 100 and then getting the cost price for the assumed selling price.
It is important to note that we need to add sales tax on the selling price after profit but not on the cost price because the selling price after profit will be the new cost price on which sales tax is being charged.