| A fruit seller buys x guavas for Rs. y and sells y guavas for Rs. x If \[x>y,\] then he made [SSC (CGL) 2012] |
A) \[\frac{{{x}^{2}}\,-\,{{y}^{2}}}{xy}\]% loss
B) \[\frac{{{x}^{2}}\,-\,{{y}^{2}}}{xy}\]% gain
C) \[\frac{{{x}^{2}}\,-\,{{y}^{2}}}{{{y}^{2}}}\]% loss
D) \[\frac{{{x}^{2}}\,-\,{{y}^{2}}}{{{y}^{2}}}\]% gain
Correct Answer: D
Solution :
| Cost price of 1 guava \[=Rs.\frac{y}{x}\] |
| Selling price of 1 guava \[=\frac{x}{y}\] |
| \[\therefore \] Profit \[=\frac{x}{y}-\frac{y}{x}=\frac{{{x}^{2}}-{{y}^{2}}}{xy}\] |
| Hence, profit per cent |
| \[=\,\frac{xy}{y/x}\,\times \,100\]%\[=\,\frac{{{x}^{2}}\,-\,{{y}^{2}}}{{{y}^{2}}}\]% |
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