Question:medium

An item is sold for 504 after allowing a 20% discount. If the shopkeeper gains 5%, then the cost price of the item is:

Updated On: Jan 16, 2026
  • \(399\)

  • \(435\)

  • \(480\)

  • \(520\)

Show Solution

The Correct Option is C

Solution and Explanation

To address this issue, we will establish variables and utilize the provided data.

  1. Denote the marked price of the item as \( M \).
  2. A 20% discount means the selling price (SP) is 80% of the marked price.

This can be expressed as:

\[ SP = \frac{80}{100} \times M = \frac{4}{5} \times M \]

Given that the selling price is 504, we set up the equation:

\[ \frac{4}{5} \times M = 504 \]

To determine \( M \), multiply both sides by \( \frac{5}{4} \):

\[ M = 504 \times \frac{5}{4} = 630 \]

Next, the shopkeeper makes a 5% profit on the cost price (CP), meaning the selling price is 105% of the cost price.

\[ SP = \frac{105}{100} \times CP = \frac{21}{20} \times CP \]

With the selling price being 504:

\[ \frac{21}{20} \times CP = 504 \]

Solving for \( CP \) requires multiplying both sides by \( \frac{20}{21} \):

\[ CP = 504 \times \frac{20}{21} = 480 \]

This result deviates from the anticipated outcome, indicating an error in calculation. Let's review and proceed with the steps accurately.

The correct cost price must satisfy the profit equation as originally calculated:

The correct computation indicates that the \( SP \) yields the \( CP \) as initially determined:

\[ SP = 504, \ CP = \frac{SP \times 100}{105} \]

\[ CP = \frac{504 \times 100}{105} = 480 \]

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