Marked Price Calculation Based on Discount Difference

This solution explains how to find the marked price (MP) using the difference between selling prices (SP) derived from different discount schemes.

Discount Schemes Compared

The problem involves two discount scenarios applied to the same marked price:

• Scenario A: A single discount of 45%.
• Scenario B: Two successive discounts of 30% and 20%.

Selling Price Calculation (Scenario A)

Calculate the selling price ($SP_A$) with a single 45% discount.

• The discount amount is $0.45 \times MP$.
• $SP_A = MP - (0.45 \times MP) = MP \times (1 - 0.45)$
• $SP_A = 0.55 \times MP$

Selling Price Calculation (Scenario B)

Calculate the selling price ($SP_B$) with successive 30% and 20% discounts.

• After the first discount (30%), the price becomes $ MP \times (1 - 0.30) = 0.70 \times MP $.
• After the second discount (20%) on the reduced price, the final selling price is:
• $SP_B = (0.70 \times MP) \times (1 - 0.20) = (0.70 \times MP) \times 0.80$
• $SP_B = 0.56 \times MP$

Marked Price Determination Using Difference

The difference between the two selling prices ($SP_B$ and $SP_A$) is given as ₹84.

• Difference = $SP_B - SP_A$
• $₹84 = (0.56 \times MP) - (0.55 \times MP)$
• $₹84 = MP \times (0.56 - 0.55)$
• $₹84 = MP \times 0.01$
• To find the marked price, rearrange the equation:
• $MP = \frac{₹84}{0.01}$
• $MP = ₹84 \times 100$
• $MP = ₹8,400$

Marked Price Value Revealed

The marked price is ₹8,400.