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Question

Answers

A. \[43\% \]

B. \[30\% \]

C. \[20\% \]

D. \[31\% \]

Answer
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It is given that; a shopkeeper fixes the MP of an item \[35\% \] above the CP. We have to find the percentage of discount that the shopkeeper allowed to gain \[8\% \].

Let us consider, the cost price of the item is \[Rs.{\rm{ }}x\].

The market price of the item is \[35\% \] above the cost price.

That is marked price of the given item is found using the formula \[\dfrac{{100 + b}}{{100}} \times {\rm{cost price}}\] where b is the percentage of the marked price.

By using the formula the marked price of the item will be\[\dfrac{{100 + 35}}{{100}} \times x = \dfrac{{135x}}{{100}}\].

Now, it is given that the shopkeeper wants to gain \[8\% \].

Hence the selling price of the item is given using the formula \[\dfrac{{100 + b}}{{100}} \times {\rm{cost price}}\] where b is the percentage of the gain.

By using the above formula we get,

The selling price of the item will be\[\dfrac{{100 + 8}}{{100}} \times x = \,\,\dfrac{{108x}}{{100}}\].

Now we have to find the amount of discount using the formula,

\[{\rm{marked price - selling price = discount}}\]

Therefore the discount amount of the item is\[\dfrac{{135x}}{{100}} - \dfrac{{108x}}{{100}} = \dfrac{{27x}}{{100}}\].

Now we have to find the percentage of discount for that we use the following formula,

\[{\rm{discount\% = }}\dfrac{{{\rm{discount}}}}{{{\rm{marked price}}}} \times 100\]

Therefore the percentage of discount is \[\dfrac{{\dfrac{{27x}}{{100}}}}{{\dfrac{{135x}}{{100}}}} \times 100\% \]

On solving the percentage we get,

\[\dfrac{{\dfrac{{27x}}{{100}}}}{{\dfrac{{135x}}{{100}}}} \times 100\% = \dfrac{{27x}}{{100}} \times \dfrac{{100}}{{135x}} \times 100 = \dfrac{{100}}{5} = 20\% \]

The percentage of discount offered to gain \[8\% \] profit is \[20\% .\]

Let us consider, the cost price of the item is \[Rs.{\rm{ }}100\].The marked price of the item is \[35\% \] above the cost price.

So, the marked price of the item will be \[Rs.{\rm{ }}135\].

Now, the shopkeeper wants to gain \[8\% \].

So, the selling price of the item will be \[Rs.{\rm{ }}100 + 8 = Rs.{\rm{ }}108\]

So, he has to give the discount of \[Rs.\,135 - 108 = Rs.{\rm{ }}27\]

Then, the percentage of discount is \[\dfrac{{27}}{{135}} \times 100\% \]

Simplifying we get, the percentage of discount is \[20\% .\]