Question

A trader buys an article for Rs. 1700 at a discount of 15% on its printed price. He raises the printed price of the article by 20% and then sells it for Rs. 2688 including sales tax on the new market price. Find:
(i) the rate of sales tax
(ii) the trader's profit as per cent.
 (a) (i) 10% (ii) \[36\dfrac{1}{{11}}\% \]
 (b) (i) 12% (ii) \[41\dfrac{3}{{17\% }}\]
 (c) (i) 14% (ii) \[47\dfrac{5}{{19}}\% \]
 (d) (i) 16% (ii) \[53\dfrac{7}{{12}}\% \]

Answer 1

Hint: To find the rate of sales tax, we will first find out the printed price of the article and then we will increase the printed price by 20%. Then we will subtract this printed price from 2688 and then we will divide it by 100 to obtain the rate of sales tax. To find the profit per cent, we will apply formula:
               \[\% {\rm{ Profit }} = \dfrac{{{\rm{Selling Price}}--{\rm{Cost Price }}}}{{{\rm{Cost Price}}}}\]

Complete step-by-step answer:
We will first find out the value of printed price with the help of data given in the question. In the question, it is given that, when a 15% discount is applied to the printed price, the printed price we get is Rs.1700. Let the value of printed price be x. Then according to question, we get:

\[ \Rightarrow \,\,\,x - \left( {15\% \,of\,x} \right) = 1700\]
\[ \Rightarrow \,\,\,x - \left( {\dfrac{{15}}{{100}} \times x} \right) = 1700\].
\[ \Rightarrow \,\,\,x - \dfrac{{15x}}{{100}} = 1700\]
\[ \Rightarrow \,\,\,\dfrac{{100x - 15x}}{{100}} = 1700\]
\[ \Rightarrow \,\,\,\dfrac{{85x}}{{100}} = 1700\]
\[ \Rightarrow \,\,\,x = \dfrac{{1700 \times 100}}{{85}}\]
\[ \Rightarrow \,\,\,x = Rs.2000\]
Thus, the value of printed price is Rs.2000. Now, there are two parts of the question, so we will calculate each part separately.

(i) Calculation of rate of sales tax :
We are given the question that the trader is raising the price of the article by 20%. So the final price of article become
Final price = (Actual printed price)+(20% of printed price)
Final Price = \[{\rm{2}}000 + {\rm{ }}\left( {{\rm{2}}0\% {\rm{ of 2}}000} \right)\]
 Final price = \[{\rm{2}}000 + \left( {\dfrac{{20}}{{100}}\, \times {\rm{2}}000} \right)\]
 Final price = \[{\rm{2}}000 + {\rm{4}}00\]
 Final = Rs \[{\rm{24}}00\]
Now, it is given that, due to addition of taxes, the selling price is increased to Rs 2688 So we get the following equation:
      Selling price = (Final Price)+(Tax)
\[{\rm{2688}} = {\rm{24}}00{\rm{ }} + \]Tax
Tax = \[{\rm{2688}} - {\rm{24}}00\]
Tax = Rs. \[{\rm{248}}\]
Now, we have to find out percent of this tax. This is given by:
Tax% = \[\dfrac{{Tax}}{{Final\,\,\Pr ice}} \times 100\]
Tax% =\[\dfrac{{248}}{{2400}}\, \times 100\]
Tax% =\[12\% \]

(ii) Calculation of profit percentage :
In the previous part, we can see that the selling price is greater than the cost price, so the trader will have a profit The profit will be given by :
Profit= Selling Price - Cost Price
Profit= \[{\rm{Rs}}.{\rm{ 24}}00--{\rm{Rs}}.{\rm{ 17}}00\]
Profit= Rs.\[{\rm{7}}00\]
Now, the percentage of profit is obtained by the formula:
\[{\rm{ \% Profit = }}\dfrac{{{\rm{Profit}}}}{{Cost{\rm{ Price}}}} \times {\rm{100}}\]
\[{\rm{ \% Profit = }}\dfrac{{700}}{{1700}} \times {\rm{100}}\]
\[{\rm{ \% Profit = }}\dfrac{{700}}{{17}}{\rm{\% }}\]
\[{\rm{ \% Profit = }}\left( {\dfrac{{697 + 3}}{{17}}} \right){\rm{ \% }}\]
\[{\rm{ \% Profit = }}\left( {\dfrac{{697}}{{17}} + \dfrac{3}{{17}}} \right)\,\% \]
\[{\rm{ \% Profit = }}\left( {41 + \dfrac{3}{{17}}} \right)\,\% \]
\[{\rm{ \% Profit = }}41\dfrac{3}{{17}}\% \]

So, the correct answer is “Option B”.

Note: We can't use the selling price as Rs. 2688 as given in question because in this selling price, the tax is also included which is not adding to the profit of the trader. So we have used the tax-free selling price.