A seller has two articles 'M' and 'N' whose cost prices are Rs. 4,000 and Rs. 8,000, respectively. He sold article 'M' after marking it 'x%' above its cost price while he marked article 'N' at '2x%' above its cost price and sold it after allowing a discount of 'x%'. The profit earned on article 'N' was 40% more than that on article 'M'. If the cost price of article 'O' is Rs. 10,000 and it is sold at a profit of '0.5x%', then find the selling price of article 'O'.

Marked price of article 'M' = 4000 × {(100 + x)/100} = Rs. (4000 + 40x) So, profit earned on article 'M' = 4000 + 40x − 4000 = Rs. 40x Marked price of article 'N' = 8000 × {(100 + 2x)/100} = Rs. (8000 + 160x) And selling price of article 'N' = (8000 + 160x) × {(100 − x)/100} = Rs. {8000 + 80x − 1.6x²} So, profit earned on article 'N' = {8000 + 80x − 1.6x²} − 8000 = Rs. (80x − 1.6x²) ATQ; (80x − 1.6x²) = 40x × 1.40 Or, 80x − 1.6x² = 56x Or, 24x = 1.6x² So, x = 24/1.6 = 15 Profit percentage on article 'O' = 15 × 0.5 = 7.5% So, Selling price of article 'O' = 10000 × (1 + 7.5/100) = Rs. 10,750