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Selling price: It is nothing but the price at which the product or service is sold to the buyer.

Given: The cash difference between the selling prices of an article at a profit of $4%$ and $6%$ is $Rs\text{ 3}$.

Required Formula:

Selling Price=$\dfrac{100+(profit\,\%)}{100}\times \cos t\text{ }price$

Let the cost price of an article be $x$.

Selling Price of an article sold at a profit of $4%$$={{S}_{1}}$

Selling Price of an article sold at a profit of $6%$$={{S}_{2}}$

According to the question,

$\begin{align}

& {{S}_{1}}=\dfrac{104}{100}x \\

& {{S}_{2}}=\dfrac{106}{100}x \\

\end{align}$

Since the cash difference between the selling prices of an article at a profit of $4%$ and $6%$ is $Rs\text{ 3}$.

$\begin{align}

& \Rightarrow {{S}_{2}}-{{S}_{1}}=3 \\

& \Rightarrow \dfrac{106}{100}x-\dfrac{104}{100}x=3 \\

& \Rightarrow \dfrac{2x}{100}=3 \\

& \Rightarrow x=150 \\

\end{align}$

Ratio of ${{S}_{1}}\text{ }to\text{ }{{S}_{2}}$ becomes

$\begin{align}

& \Rightarrow \dfrac{{{S}_{1}}}{{{S}_{2}}}=\dfrac{\dfrac{104x}{100}}{\dfrac{106x}{100}} \\

& \Rightarrow \dfrac{{{S}_{1}}}{{{S}_{2}}}=\dfrac{104}{106} \\

& \Rightarrow \dfrac{{{S}_{1}}}{{{S}_{2}}}=\dfrac{52}{53} \\

\end{align}$

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