A bicycle was sold at a profit of $12 %$ Had it been sold for $R s . 16$ more the profit would have been $20 %$ . Find the selling price of the bicycle.

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Solution

Let the $C P$ and $S P$ of the bicycle be $x$ and $y$ respectively.

For the case, when $S P = y,$
$\begin{matrix} gain % & = \frac{S P - C P}{C P} \times 100 12 & = \frac{y - x}{x} \times 100 0.12 x & = y - x y & = 1.12 x \dots (i) \end{matrix}$

For the case, when $S P = y + 16,$
$\begin{matrix} gain % & = \frac{S P - C P}{C P} \times 100 20 & = \frac{y + 16 - x}{x} \times 100 0.2 x & = 1.12 x + 16 - x 0.2 x & = 0.12 x + 16 0.08 x & = 16 x & = R s . 200 \end{matrix}$

By using equation $(i),$
$\begin{matrix} y & = 1.12 x = 1.12 \times 200 = R s . 224 \end{matrix}$

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A bicycle was sold at a profit of 12% Had it been sold for Rs. 16 more the profit would have been 20%. Find the selling price of the bicycle.

Let the CP and SP of the bicycle be x and y respectively.For the case, when SP=y,gain %=SP−CPCP×10012=y−xx×1000.12x=y−xy=1.12x…(i)For the case, when SP=y+16,gain %=SP−CPCP×10020=y+16−xx×1000.2x=1.12x+16−x0.2x=0.12x+160.08x=16x=Rs. 200By using equation (i),y=1.12x=1.12×200=Rs. 224

A bicycle was sold at a profit of $12 %$ Had it been sold for $R s . 16$ more the profit would have been $20 %$ . Find the selling price of the bicycle.