Question

A furniture was sold for 1,10,000 with a profit of 10%. If it were sold for 80,000 rupees, then what would have been the percentage of profit/loss?

• A. 10% Loss
• B. 5% Profit
• C. 20% Loss
• D. 8% Loss

Hint:

For profit/loss calculations, it's often easiest to work with multipliers. A 10% profit means the selling price is \(100% + 10% = 110%\) or 1.1 times the cost price. To find the cost price, you simply divide the selling price by this multiplier.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem
We are given the selling price (SP) and the profit percentage. We need to find the cost price (CP) first. Then, using this CP, we need to calculate the profit or loss percentage for a new selling price.

Step 2: Key Formula or Approach
\begin{enumerate}
Cost Price (CP) = \( \frac{\text{Selling Price (SP)}}{1 + (\text{Profit}%/100)} \).
Loss = CP - New SP.
Loss Percentage = \( \frac{\text{Loss}}{\text{CP}} \times 100% \). \end{enumerate}
Step 3: Detailed Explanation
1. Find the Cost Price (CP):
Initial SP = 1,10,000
Profit = 10% = 0.10
The formula connecting SP, CP, and profit is \( SP = CP \times (1 + \text{Profit}%) \).
\[ 1,10,000 = CP \times (1 + 0.10) \] \[ 1,10,000 = CP \times 1.1 \] \[ CP = \frac{1,10,000}{1.1} = \frac{11,00,000}{11} = 1,00,000 \] So, the cost price of the furniture was 1,00,000 rupees.
2. Calculate Profit/Loss with the New Selling Price:
New SP = 80,000 rupees
CP = 1,00,000 rupees
Since the New SP (80,000) is less than the CP (1,00,000), there is a loss.
\[ \text{Loss} = CP - \text{New SP} = 1,00,000 - 80,000 = 20,000 \text{ rupees} \] 3. Calculate the Loss Percentage:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{CP}} \times 100% \] \[ \text{Loss Percentage} = \frac{20,000}{1,00,000} \times 100% \] \[ \text{Loss Percentage} = \frac{1}{5} \times 100% = 20% \]
Step 4: Final Answer
If the furniture were sold for 80,000 rupees, there would be a 20% loss. Therefore, option (C) is the correct answer.