Question

If A % is the discount on the marked price Y , the discount is

• A. (A/Y)x 100
• B. 100/A + Y
• C. (A/100) x Y
• D. (Y/A) X 100

Hint:

Remember the definition of percent: "per cent" literally means "per 100."
Therefore, any percentage $A\%$ is mathematically written as $\frac{A}{100}$. Multiplying this by the principal value $Y$ gives the final amount: $\frac{A}{100} \times Y$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In commercial transactions, the price printed on an item is called the marked price (or list price).
A discount is a price reduction offered to buyers, usually expressed as a percentage of this marked price.
The actual discount value is calculated by converting the discount percentage into a decimal or fraction and multiplying it by the marked price.
Key Formula or Approach:
The mathematical formula to find the discount value is: \[ \text{Discount} = \text{Discount Percentage} \times \text{Marked Price} \] To convert a percentage $P\%$ into a standard mathematical fraction, we divide by 100: \[ P\% = \frac{P}{100} \]

Step 2: Detailed Explanation:
Let us use the values provided in the question:
- Marked Price $= Y$
- Discount Percentage $= A\%$
Convert the discount percentage $A\%$ into a mathematical fraction: \[ A\% = \frac{A}{100} \] Now, multiply this fraction by the marked price $Y$ to find the actual discount amount: \[ \text{Discount} = \left(\frac{A}{100}\right) \times Y \] This can be written in algebraic form as: \[ \text{Discount} = \frac{A}{100} \times Y \] This matches the expression in option (C).

Step 3: Final Answer:
The discount on a marked price $Y$ at a rate of $A\%$ is given by the expression $\frac{A}{100} \times Y$.
Therefore, the correct option is (C).