If the selling price of 16 water bottles is equal to the cost price of 17 water bottles,

Question:

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.

Solution:

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 $=\left(\frac{\text { gain }}{\text { CP }} \times 100\right) \%$

$=\left(\frac{\mathrm{x}-\mathrm{y}}{\mathrm{y}} \times 100\right) \%$

$=\left\{\left(\frac{\mathrm{x}}{\mathrm{y}}-1\right) \times 100\right\} \%$

$=\left\{\left(\frac{17}{16}-1\right) \times 100\right\} \%$

$=\left(\frac{1}{16} \times 100\right) \%$

$=6 \frac{1}{4} \%$

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