| If a commission of 10% is given on the written price of an article, the gain is 20%. The gain per cent, when the commission is increased to 20%, will be [SSC (FCI) 2012] |
A) \[6\frac{2}{3}\]%
B) 5%
C) 8%
D) \[5\frac{1}{3}\]%
Correct Answer: A
Solution :
| Let MP of the article be Rs. x. |
| \[\therefore \] SP of the article \[=\frac{x\times (100-10)}{100}=Rs.\frac{9x}{10}\] |
| \[\Rightarrow \] CP of the article \[=\frac{9x}{10}\times \frac{100}{100+20}\] |
| \[=\frac{9x\times 10}{120}=Rs.\frac{3x}{4}\] |
| Now, new SP of the article |
| \[=\frac{x\times (100-20)}{100}=Rs.\frac{4x}{5}\] |
| \[\Rightarrow \] New profit |
| \[=\left( \frac{4x}{5}-\frac{3x}{4} \right)=\frac{16x-15x}{20}=Rs.\frac{x}{20}\] |
| Hence, profit per cent \[=\,\,\frac{\frac{x}{20}}{\frac{3x}{4}}\times 100%\] |
| \[=\frac{4\times 100}{3\times 20}%=6\frac{2}{3}\]% |
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