Question

Renu sold an article at a loss of 8%. Had she bought it at 10% less and sold for Rs 36 more; she would have gained 20%. Find the cost price of the article

Answer 1

$let \: cp = x \\ sp = x - \frac{8x}{100} = \frac{92x}{100} \\ if \: \:new \: cp = \: x - \frac{10x}{100} = \frac{9x}{10} \\ new \: sp = \frac{92x}{100} + 36 \\ p = sp - cp \\ 20\% \: of \: \frac{9x}{10} = \frac{92x}{100} + 36 - \frac{9x}{10} \\ \frac{20 \times 9x}{100 \times 10} = \frac{92x - 90x}{100} + 36 \\ \frac{9x}{50} = \frac{2x}{100} + 36 \\ \frac{ 9x }{50} - \frac{2x}{100} = 36 \\ \frac{9x - x}{50} = 36 \\ 8x = 36 \times 50 \\ x = \frac{36 \times 50}{8} \\ x = 225$