Math Problem Statement

A shopkeeper marked an item % above its cost price and sold it at 7.5% profit. The cost price of the item was Rs. 336 and approximately % discount was given on its marked price. Had marked price of the item been Rs. 44 less, then discount would have been Rs 391/3 at the same discount percentage

Which of the following options will fill the blanks in same order?

Solution

To solve the problem step by step, we will determine the missing percentage and validate the scenario described.


Step 1: Define variables and relationships

  • Cost Price (CP): Rs.336Rs. 336
  • Marked Price (MP): Let the marked price be xx.
  • Discount Percentage (D%): Let the discount percentage be d%d \%.
  • Selling Price (SP): The selling price is CP+7.5% of CPCP + 7.5\% \text{ of } CP.

Step 2: Calculate Selling Price (SP)

SP=CP+7.5%×CP=336+0.075×336=336+25.2=Rs.361.2SP = CP + 7.5\% \times CP = 336 + 0.075 \times 336 = 336 + 25.2 = Rs. 361.2


Step 3: Relate SP, MP, and discount

The selling price is derived from the marked price after applying the discount: SP=MP×(1d100)SP = MP \times \left(1 - \frac{d}{100}\right) Substituting SP=361.2SP = 361.2: 361.2=x×(1d100)361.2 = x \times \left(1 - \frac{d}{100}\right)


Step 4: Relate discount with given condition

If the marked price is reduced by Rs.44Rs. 44, the discount becomes Rs.391/3=130.33Rs. 391/3 = 130.33. The new marked price is x44x - 44, so: Discount=(x44)×d100=130.33\text{Discount} = (x - 44) \times \frac{d}{100} = 130.33

This gives: [ (x - 44) \times d = 13033

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Math Problem Analysis

Mathematical Concepts

Profit and Loss
Discount Calculation
Linear Equations

Formulas

Selling Price (SP) = Cost Price (CP) + (Profit Percentage × CP)
SP = Marked Price (MP) × (1 - Discount Percentage / 100)
Discount = MP × (Discount Percentage / 100)

Theorems

Proportionality relationships in percentage problems

Suitable Grade Level

Grades 9-12