A person sells a watch at a profit of 26 %. If he had bought...

A person sells a watch at a profit of $26 \%$. If he had bought it at $20 \%$ less and sold for Rs. 81.60 less, he would have gained $32 \%$. What is the original cost price (in Rs.) of the watch?
(a) 400
(b) 480
(c) 450
(d) 360

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Key Concepts

Relationship Between Cost Price and Selling Price

The relationship between cost price and selling price is fundamental in commercial transactions. This concept involves understanding that the selling price is derived from the cost price by adding the profit margin, and any changes in either value directly affect the profit percentage.

Percentage Change Adjustments

Percentage change adjustments refer to modifications made to a base value by a given percentage. In this context, it involves decreasing the cost price by a certain percentage and adjusting the selling price accordingly, which is crucial for setting up equations that capture the modified profit conditions.

Profit Percentage

Profit percentage is the ratio of the profit earned to the cost price, expressed as a percentage. It indicates how much gain is made compared to the amount invested, and understanding it is essential for determining selling price or cost price when one of the values is unknown.

Algebraic Equation Formulation

Algebraic equation formulation is the process of converting word problems into mathematical equations using variables. This technique allows one to represent conditions such as modified cost prices and selling prices, and thus solve for unknowns by analyzing the relationships dictated by profit percentages.

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