If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.
Let Rs $x$ be the SP of each bottle and Rs $y$ be the CP of each bottle.
SP of 16 bottles $=\mathrm{CP}$ of 17 bottles
$\Rightarrow 16 \mathrm{x}=17 \mathrm{y}$
$\Rightarrow \frac{\mathrm{x}}{\mathrm{y}}=\frac{17}{16}$ Gain per bottle
$=\mathrm{SP}-\mathrm{CP}$ $=\mathrm{Rs}(\mathrm{x}-\mathrm{y})$
$=\operatorname{Rs}(x-y)$
$\therefore$ Gain percentage $=\left(\frac{\text { gain }}{\text { CP }} \times 100\right) \%$
$=\left(\frac{\mathrm{x}-\mathrm{y}}{\mathrm{y}} \times 100\right) \%$
$=\left\{\left(\frac{\mathrm{x}}{\mathrm{y}}-1\right) \times 100\right\} \%$
$=\left\{\left(\frac{17}{16}-1\right) \times 100\right\} \%$
$=\left(\frac{1}{16} \times 100\right) \%$
$=6 \frac{1}{4} \%$