Discussion
A sells an item to B at a profit of 10%. B sells the item back to A at a loss of 10 %. What is correct statement about this transaction?
Answer: D
The correct statement is that A makes a profit of 11%.
Let A's cost be Rs 100. A sells to B at 10% profit, for Rs 110. B sells it back at a 10% loss on Rs 110, for Rs 99.
\[ \begin{aligned} \text{A receives} &= 110, \quad \text{A pays} = 99 \\ \text{A's gain} &= 110 - 99 = 11 \end{aligned} \]
A ends with the item back and Rs 11 more than before, a profit of 11 on the original 100, which is 11%. A did not break even, and 20% comes from simply adding the two percentages. B lost Rs 11 on a Rs 110 outlay, which is 10%, not 20%.
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