Question

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

• A. \(399\)
• B. \(435\)
• C. \(480\)
• D. \(520\)

Answer 1

The Correct Option is C

To solve this problem, let's define some variables and use the given data.

1. Let the marked price of the item be \( M \).
2. The discount is 20%, implying the selling price (SP) is 80% of the marked price.

So, we have:

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

Given that the selling price is 504, we can write:

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

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

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

Now, the shopkeeper gains 5% on the cost price (CP). Hence, the selling price is 105% of the cost price.

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

Since the selling price is 504:

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

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

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

However, this doesn't match our expected result, indicating a miscalculation. To correct, reassess and follow through the steps properly:

The correct cost price should fulfill the gain equation properly:

Correct calculation states: the \( SP \) yields \( CP \) as originally calculated:

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

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