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: Conceptualization:
This problem requires calculating profit percentage. Profit percentage is computed based on the cost price (the price Ram paid for the watch), not the initial price.
Profit = Selling Price (SP) - Cost Price (CP)
Profit % = \( \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \)

Step 2: Methodology:
Assume the original cost of the watch is Rs. 100 for simplified calculation.
1. Determine Ram's Cost Price (CP).
2. Determine Ram's Selling Price (SP).
3. Calculate the profit amount.
4. Calculate the profit percentage.

Step 3: Detailed Calculation:
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% above the original cost = Original Cost + 8% of Original Cost.
SP = \( 100 + \left(\frac{8}{100} \times 100\right) = 100 + 8 = \text{Rs. } 108 \).
Calculate the profit:
Profit = SP - CP = \( 108 - 90 = \text{Rs. } 18 \).
A positive result indicates a profit.
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: Conclusion:
Ram achieved a profit of 20%.