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Question

Answers

(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
Verified

\[\% {\rm{ Profit }} = \dfrac{{{\rm{Selling Price}}--{\rm{Cost Price }}}}{{{\rm{Cost Price}}}}\]

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:

\[{\rm{ \% Profit = }}\dfrac{{{\rm{Profit}}}}{{Cost{\rm{ Price}}}} \times {\rm{100}}\]

\[{\rm{ \% Profit = }}\dfrac{{700}}{{1700}} \times {\rm{100}}\]

\[{\rm{ \% Profit = }}\dfrac{{700}}{{17}}{\rm{\% }}\]

\[{\rm{ \% Profit = }}\left( {\dfrac{{697 + 3}}{{17}}} \right){\rm{ \% }}\]

\[{\rm{ \% Profit = }}\left( {\dfrac{{697}}{{17}} + \dfrac{3}{{17}}} \right)\,\% \]

\[{\rm{ \% Profit = }}\left( {41 + \dfrac{3}{{17}}} \right)\,\% \]

\[{\rm{ \% Profit = }}41\dfrac{3}{{17}}\% \]