This problem requires calculating the selling price of a book in one store given information about its selling price in another store and the ratio of their discount percentages. The table provides context about discounts offered by different stores on various books, but the specific discount percentages for Book C in Store 1 and Store 2 are not directly listed. However, we are given that the ratio of discount percentages for Book C in Store 1 ($D_1$) to Store 2 ($D_2$) is $3:2$. We are also told that the marked price (MP) for every book is the same across all stores. The selling price in Store 1 ($SP_1$) is given as $₹220$, and we need to find the approximate selling price in Store 2 ($SP_2$).

Understanding Selling Price and Discount Relationships

The fundamental relationship between Selling Price (SP), Marked Price (MP), and Discount Percentage (D) is:

$ SP = MP - \text{Discount} $

Where the Discount amount is calculated as:

$ \text{Discount} = MP \times \frac{D}{100} $

Substituting the discount amount into the SP formula, we get:

$ SP = MP - \left( MP \times \frac{D}{100} \right) $

Factoring out MP:

$ SP = MP \times \left( 1 - \frac{D}{100} \right) $

Calculating Discount Percentages

We are given that the ratio of discount percentages for Book C in Store 1 and Store 2 is $3:2$. Let the discount percentages be $D_1$ and $D_2$ respectively.

$ \frac{D_1}{D_2} = \frac{3}{2} $

We can represent these percentages using a common factor, say $k$. Let $D_1 = 3k$ and $D_2 = 2k$.

Now, we apply the selling price formula for both stores:

For Store 1: $SP_1 = MP \times (1 - D_1/100)$

$ 220 = MP \times \left( 1 - \frac{3k}{100} \right) $

For Store 2: $SP_2 = MP \times (1 - D_2/100)$

$ SP_2 = MP \times \left( 1 - \frac{2k}{100} \right) $

To find $SP_2$, we need to determine the value of $k$ or find the MP. Let's find a relationship between $SP_1$ and $SP_2$ by dividing the two equations:

$ \frac{SP_1}{SP_2} = \frac{MP \times (1 - D_1/100)}{MP \times (1 - D_2/100)} $

$ \frac{220}{SP_2} = \frac{1 - 3k/100}{1 - 2k/100} = \frac{(100 - 3k)/100}{(100 - 2k)/100} = \frac{100 - 3k}{100 - 2k} $

This equation has two unknowns ($SP_2$ and $k$). We can solve this by checking the options provided for $SP_2$. Let's test Option 2, where $SP_2 = ₹230$:

$ \frac{220}{230} = \frac{100 - 3k}{100 - 2k} $

$ \frac{22}{23} = \frac{100 - 3k}{100 - 2k} $

Cross-multiply to solve for $k$:

$ 22 \times (100 - 2k) = 23 \times (100 - 3k) $

$ 2200 - 44k = 2300 - 69k $

Rearrange the terms:

$ 69k - 44k = 2300 - 2200 $

$ 25k = 100 $

$ k = \frac{100}{25} = 4 $

With $k=4$, the discount percentages are:

$ D_1 = 3k = 3 \times 4 = 12\% $

$ D_2 = 2k = 2 \times 4 = 8\% $

These are valid discount percentages.

Determining the Marked Price

Now that we have $D_1 = 12\%$ and $SP_1 = ₹220$, we can calculate the Marked Price (MP):

$ SP_1 = MP \times \left( 1 - \frac{D_1}{100} \right) $

$ 220 = MP \times \left( 1 - \frac{12}{100} \right) $

$ 220 = MP \times (1 - 0.12) $

$ 220 = MP \times 0.88 $

$ MP = \frac{220}{0.88} $

To simplify the division:

$ MP = \frac{22000}{88} = \frac{11000}{44} = \frac{5500}{22} = \frac{2750}{11} = 250 $

So, the Marked Price (MP) of the book is $₹250$.

Finding the Selling Price in Store 2

We can now calculate the selling price in Store 2 ($SP_2$) using the Marked Price ($MP = ₹250$) and the discount percentage for Store 2 ($D_2 = 8\%$).

$ SP_2 = MP \times \left( 1 - \frac{D_2}{100} \right) $

$ SP_2 = 250 \times \left( 1 - \frac{8}{100} \right) $

$ SP_2 = 250 \times (1 - 0.08) $

$ SP_2 = 250 \times 0.92 $

Calculating the product:

$ SP_2 = 230 $

Thus, the approximate selling price in Store 2 is $₹230$.