Question

A shopkeeper offers a discount of $22%$ on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of $26%$ on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is:

Hint:

When a shopkeeper gives more items than charged (like “13 for the price of 12”), treat all given items as contributing to total cost but only the charged items as contributing to revenue.

Answer 1

Correct Answer: 175

Step 1: For 13 chairs, total cost price \(= 13 \times 100 = 1300\). A 26% profit means total revenue must be \(1300 \times 1.26 = 1638\).
Step 2: This revenue comes from selling 13 chairs at the discounted price of only 12 chairs, i.e. revenue \(= 12 \times (0.78M)\), where \(M\) is the marked price.
Step 3: Set the two equal: \(12 \times 0.78M = 1638 \Rightarrow 9.36M = 1638 \Rightarrow M = \dfrac{1638}{9.36} = 175\).
\[ \boxed{M = \text{Rs } 175} \]