Question

Rajnish bought an item at 25% discount on the printed price. He sold it at a 10% discount on the printed price. What is his profit in percentage?

• A. 10
• B. 15
• C. 17.5
• D. 20
• E. None of the above

Answer 1

The Correct Option is D

To determine Rajnish's percentage profit, we need to analyze both the cost price (CP) and the selling price (SP) based on the discounts given.

1. Let's assume the printed price of the item is \(P\).
2. Rajnish bought the item at a 25% discount on the printed price. Therefore, the cost price (CP) is calculated as follows: 
   \(CP = P - 0.25 \times P = 0.75 \times P\)
3. He sold the item at a 10% discount on the printed price. Therefore, the selling price (SP) is: 
   \(SP = P - 0.10 \times P = 0.90 \times P\)
4. Profit is given by the difference between the selling price and the cost price: 
   \(Profit = SP - CP = (0.90P - 0.75P) = 0.15P\)
5. The profit percentage is calculated as 
   \(Profit \, Percentage = \left( \frac{Profit}{CP} \right) \times 100 = \left( \frac{0.15P}{0.75P} \right) \times 100\)
   \(= \left( \frac{0.15}{0.75} \right) \times 100 = 20\%\)

Thus, the profit percentage when Rajnish sells the item is 20%.

Answer 2

To solve this problem, we need to calculate the cost price (CP) and the selling price (SP) of the item using the given discounts and then derive the profit percentage.

Steps to find the solution:

1. Let the printed price of the item be \( P \).
2. Rajnish bought it at a 25% discount, so his cost price is:
   \( \text{CP} = P - 0.25P = 0.75P \).
3. He sold it at a 10% discount on the printed price, so the selling price is:
   \( \text{SP} = P - 0.10P = 0.90P \).
4. Profit made is given by:
   \( \text{Profit} = \text{SP} - \text{CP} = 0.90P - 0.75P = 0.15P \).
5. Profit Percentage is calculated as:
   \[ \text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{0.15P}{0.75P}\right) \times 100 = 20\% \]

The profit percentage Rajnish made is 20%.