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Question

Answers

\[A)\] \[3.13\]

\[B)\] \[5.26\]

\[C)\] \[4.17\]

\[D)\] \[5.89\]

Answer

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Selling price of the same thing $ = y$

So the profit income is equal to (Selling price – Cost price)$ = \left( {y - x} \right)$

So the profit percentage earned is equal to ${\text{ = }}\left( {\dfrac{{{\text{profit income }} \times 100}}{{{\text{cost price}}}}} \right)$

Let us consider the selling price of the material is $100$ unit.

It is given in the question that the cost price of the material is $96\% $ of the selling price.

So, the cost price of the same material is $ = 96\% $ of $100$

So, the cost price $ = \dfrac{{96}}{{100}} \times 100 = 96$ unit

Now we have to find profit made by selling the material is = (Selling price – Cost price)$ = \left( {100 - 96} \right) = 4$ unit

So, the profit percentage earned by selling the material is ${\text{ = }}\left( {\dfrac{{{\text{profit income}} \times 100}}{{{\text{cost price}}}}} \right)$

$ \Rightarrow \dfrac{{4 \times 100}}{{96}}$

On rewriting we get

\[ \Rightarrow \dfrac{{400}}{{96}}\]

Let us divide the term and we get,

\[ \Rightarrow 4.16667\]

Take as approximately we get

\[ \approx 4.17.\]

So, the profit earned is \[4.17\% \].

Let us consider the selling price of the material is \[s.\]

So, the cost price of the material is \[96\% \] of the selling price.

So, the cost price is \[ = 96\% \] of \[s\]\[ = \dfrac{{96}}{{100}} \times s = 0.96s.\]

So, the profit made by selling the material is \[ = (s - 0.96s) = 0.04s.\]

So, the profit percentage earned is \[ = \dfrac{{profit \times 100}}{{\cos t\_price}}.\]

Profit percentage earned is

\[ \Rightarrow \dfrac{{0.04s \times 100}}{{0.96s}}.\]

On multiply the numerator term and we get,

\[ \Rightarrow \dfrac{{4s}}{{0.96s}}.\]

We split the denominator term and we can write it as

\[ \Rightarrow \dfrac{{4s \times 100}}{{96s}}.\]

On cancel the same term and we get

\[ \Rightarrow \dfrac{{4 \times 100}}{{96}}.\]

On simplification we get

\[ \approx 4.17.\]

Always remember, when a shopkeeper makes profit by selling any material, it states that the value of the selling price is always greater than the value of the cost price.

If the selling price is less than the cost price, it states that the shopkeeper is making a loss by selling the same material.