Calculating Wardrobe Discount Percentage

This problem involves finding the discount percentage applied to a wardrobe. We are given the marked price (MP), the percentage by which the marked price exceeds the cost price (CP), and the profit percentage achieved on the sale.

Step 1: Determine the Cost Price (CP)

The marked price (MP) of the wardrobe is given as ₹668. It is stated that this marked price is 22% above the cost price (CP). This relationship can be expressed mathematically:

\(MP = CP \times (1 + \frac{22}{100})\)

\(MP = CP \times (1 + 0.22)\)

\(MP = CP \times 1.22\)

Now, we substitute the known value of the marked price:

\(₹668 = CP \times 1.22\)

To find the cost price, we rearrange the equation:

\(CP = \frac{₹668}{1.22}\)

Calculating this value gives us the cost price:

\(CP \approx ₹547.54098\)

Step 2: Calculate the Selling Price (SP)

The question mentions that the profit percentage is 7%. The selling price (SP) is calculated based on the cost price plus the profit earned:

\(SP = CP + (CP \times \frac{7}{100})\)

\(SP = CP \times (1 + 0.07)\)

\(SP = CP \times 1.07\)

Using the cost price calculated in the previous step:

\(SP = \left( \frac{₹668}{1.22} \right) \times 1.07\)

\(SP \approx ₹547.54098 \times 1.07\)

Performing the multiplication, we get the selling price:

\(SP \approx ₹585.86885\)

Step 3: Find the Discount Amount

The discount amount is the difference between the marked price (MP) and the selling price (SP). The formula is:

\(Discount = MP - SP\)

Substituting the values:

\(Discount \approx ₹668 - ₹585.86885\)

Calculating the difference:

\(Discount \approx ₹82.13115\)

Step 4: Compute the Discount Percentage

The discount percentage is calculated based on the marked price. The formula is:

\(Discount Percentage = \frac{Discount}{MP} \times 100\)

Plugging in the values for the discount amount and marked price:

\(Discount Percentage \approx \frac{₹82.13115}{₹668} \times 100\)

\(Discount Percentage \approx 0.122950 \times 100\)

\(Discount Percentage \approx 12.2950\%\)

Rounding the result to two decimal places, we find the discount percentage to be 12.30%.