| If the cost price of 16 pens is equal to the selling price of 12 pens, then the gain or loss per cent is |
A) \[33\frac{1}{3}%\,gain\]
B) 25% gain
C) 25% loss
D) \[33\frac{1}{3}%\,\,loss\]
Correct Answer: A
Solution :
| Given, \[\sqrt{{{(x-a)}^{2}}+{{(y-0)}^{2}}}=a+x\] |
| \[\Rightarrow \] \[{{(x-a)}^{2}}+{{y}^{2}}={{(a+x)}^{2}}\] |
| \[\Rightarrow \] \[{{x}^{2}}-2ax+{{a}^{2}}+{{y}^{2}}={{a}^{2}}+2ax+{{x}^{2}}\] |
| \[\Rightarrow \] \[{{x}^{2}}+{{a}^{2}}+{{y}^{2}}-{{a}^{2}}-{{x}^{2}}=2ax+2ax\] |
| \[\therefore \] \[{{y}^{2}}=4ax\] |
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