Question

if the cost price of 14 apples is the same as the selling price of 12 apples, find the gain percent.
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Answer 1

$cp \: of \: 14 \: apples = sp \: of \: 12 \: apples = x\\ cp \: of \: 1 \: apple = \frac{x}{14} \\ sp \: of \: 1 \: apple = \frac{x}{12} \\ gain = \frac{x}{12} - \frac{x}{14} = \frac{7x - 6x}{84} = \frac{x}{84} \\ gain\% = \frac{gain \times 100}{cp} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{x}{84} \times 100 \div \frac{x}{14} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{x \times 100 \times 14}{x \times 84} = \frac{100}{6} \% = \frac{50}{3} \%\\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 16 \frac{2}{3} \%$