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):
- Marked Price (MP): Let the marked price be .
- Discount Percentage (D%): Let the discount percentage be .
- Selling Price (SP): The selling price is .
Step 2: Calculate Selling Price (SP)
Step 3: Relate SP, MP, and discount
The selling price is derived from the marked price after applying the discount: Substituting :
Step 4: Relate discount with given condition
If the marked price is reduced by , the discount becomes . The new marked price is , so:
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
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