| A single discount equivalent to the discount series 20%, 10% and 15% is |
A) 36.1%
B) 38.8%
C) 31.6%
D) 38.2%
Correct Answer: B
Solution :
| Let the marked price be x. |
| Then, amount after discount series |
| \[=\left[ \left( x-\frac{20}{100}x \right)-\frac{10}{100}\times \left( x-\frac{20x}{100} \right) \right]\] |
| \[-\frac{15}{100}\left[ \left( x-\frac{20x}{100} \right)-\frac{1}{10}\left( x-\frac{20x}{100} \right) \right]\] |
| \[=\left[ \left( x-\frac{x}{5} \right)-\frac{1}{10}\left( x-\frac{x}{5} \right) \right]-\frac{15}{100}\left[ \frac{4x}{5}-\frac{1}{10}\left( \frac{4x}{5} \right) \right]\] |
| \[=\,\,\left[ \frac{4x}{5}-\frac{1}{10}\left( \frac{4x}{5} \right) \right]-\frac{15}{100}\left[ \frac{40x-4x}{50} \right]\] |
| \[=\frac{(40-4)x}{50}-\frac{15}{100}\left( \frac{36x}{50} \right)\] |
| \[=\frac{36x}{50}-\frac{15\times 36x}{100\times 50}=\frac{612x}{1000}\] |
| Discount\[=x-\frac{612}{1000}=\frac{388}{1000}\times 100=38.8\]% |
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