A trader marks up the price of a product by $50$%. If the discount is increased from $10$% to $20$%, his profit comes down by Rs. $105$. What is the cost price of the product?

Let the cost price be C; a 50% markup makes the marked price 1.5C. With a 10% discount, the first selling price is 1.5C * 0.9 = 1.35C. When the discount increases to 20%, the second selling price is 1.5C * 0.8 = 1.2C. The drop in profit equals the drop in selling price, so 1.35C - 1.2C = 105, which simplifies to 0.15C = 105, yielding a cost price of C = 700.

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