David owns a plot worth ₹10,000. He sells it to Rodney at 10% profit. Rodney sells the plot back to David at a

Question

David owns a plot worth ₹10,000. He sells it to Rodney at 10% profit. Rodney sells the plot back to David at a loss of 10%. In the whole transaction, Rodney realises ________.

Examoogle · Accepted Answer

The correct answer is Option D: loss of ₹1,100. Rodney buys the plot from David for 1.1 × 10,000 = 11,000 and sells it back to David for 0.9 × 11,000 = 9,900. His loss is 11,000 - 9,900 = 1,000.

Step-by-Step Solution & Concepts:
Shortcut Trick: Rodney buys the plot from David for 1.1 × 10,000 = 11,000 and sells it back to David for 0.9 × 11,000 = 9,900. His loss is 11,000 - 9,900 = 1,000.

Formula Used: $$P = CP 	imes \frac{100 + profit\%}{100}$$, $$L = CP 	imes \frac{100 - loss\%}{100}$$

Given: Initial plot worth = ₹10,000. David sells to Rodney at 10% profit. Rodney sells back to David at 10% loss.

Steps: Calculate Rodney's Cost Price: David sells the plot worth ₹10,000 to Rodney at 10% profit. Rodney's cost price $CP_{Rodney}$ is: $$10,000 	imes (1 + 0.10) = 11,000$$. Calculate Rodney's Selling Price: Rodney sells the plot back to David at a 10% loss. His selling price $SP_{Rodney}$ is: $$11,000 	imes (1 - 0.10) = 9,900$$. Calculate Rodney's Profit/Loss: Since $SP_{Rodney}

Answer: D is correct because Rodney bought the plot for ₹11,000 and sold it for ₹9,900, resulting in a loss of ₹1,000.

Exam Tip: This concept is a variation of the successive percentage change formula $$a + b + \frac{ab}{100}$$. Here, $a = 10, b = -10$, so $10 - 10 - \frac{100}{100} = -1\%$. 1% of 10,000 is 100, but since Rodney's base was 11,000, 10% loss on 11,000 is 1,100.

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