Question

Ram purchased a watch at a cost of \( \left(\frac{9}{10}\right)^{th} \) of the original cost and sold at 8% more than the original cost. His profit/loss is

• A. 20% profit
• B. 20% loss
• C. 18% profit
• D. 18% loss

Hint:

Assuming the original cost to be 100 is a very effective strategy in percentage-based problems. Always remember that profit or loss percentage is calculated on the cost price, not the marked price or original cost.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves calculating the profit percentage. Profit percentage is calculated on the cost price (the price at which Ram purchased the watch), not the original cost.
Profit = Selling Price (SP) - Cost Price (CP)
Profit % = \( \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \)
Step 2: Key Formula or Approach:
Let the original cost of the watch be Rs. 100. This makes the calculation easier.
1. Calculate Ram's Cost Price (CP).
2. Calculate Ram's Selling Price (SP).
3. Calculate the profit.
4. Calculate the profit percentage.
Step 3: Detailed Explanation:
Let the original cost be Rs. 100.
Ram's Cost Price (CP) = \( \frac{9}{10} \) of the original cost = \( \frac{9}{10} \times 100 = \text{Rs. } 90 \).
Ram's Selling Price (SP) = 8% more than the original cost = Original Cost + 8% of Original Cost.
SP = \( 100 + \left(\frac{8}{100} \times 100\right) = 100 + 8 = \text{Rs. } 108 \).
Now, calculate the profit:
Profit = SP - CP = \( 108 - 90 = \text{Rs. } 18 \).
Since the result is positive, it is a profit.
Now, calculate the profit percentage:
Profit % = \( \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \)
Profit % = \( \left(\frac{18}{90}\right) \times 100 \)
Profit % = \( \left(\frac{1}{5}\right) \times 100 = 20% \).
Step 4: Final Answer:
Ram made a 20% profit.