31. A sells a article to B at a profit of 10%, B sells the article back of A at a loss of 10%. In this transaction. (1) A neither loss nor gains (2) A makes a profit of 11% (3) A makes a profit of 20% (4) В loses 20%

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31. (2) Let ( mathrm{CP} ) of article for ( A=₹ x ) ( therefore ) SP of article for ( A=₹ x times frac{(100+10)}{100} ) ( =₹ frac{110 x}{100}=₹ frac{11 x}{10} ) Now, CP of article for ( B=₹ frac{11 x}{10} ) ( begin{aligned} therefore text { SP of article for } B &=₹ frac{11 x}{10} timesleft(frac{100-10}{100}right) &=₹ frac{11 x times 90}{100 times 10}=₹ frac{99 x}{100} end{aligned} ) Now, profit for ( A=₹left(x-frac{99 x}{100}right)+frac{x}{10} ) ( =₹ frac{x}{100}+frac{x}{10}=frac{11 x}{100} ) Hence, gain% ( =frac{11 x / 100}{x} times 100 %=11 % )

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