The marked price of a wardrobe is ₹668, which is 22% above the cost price. If the profit percentage is 7%, find the discount percentage (rounded off to two decimal places).
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%.
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
