Question

A shopkeeper offers a 22% discount on the marked price of chairs. He gives 13 chairs to a customer at the discounted price of 12 chairs. If he still makes a profit of 26%, what is the marked price (MP) of a single chair, assuming its cost price (CP) is Rupees 100?

Hint:

Reduce everything to what happens for one chair actually delivered to the customer: figure out what fraction of the marked price the shop effectively collects per chair once you combine the percentage discount with the free-chair offer, then set that equal to CP times (1 + profit fraction).

Answer 1

Correct Answer: 175

Step 1: Cost of the \(13\) chairs given away \(=13\times100=1300\). For a \(26\%\) profit, the total revenue collected must be \(1300\times1.26=1638\).
Step 2: The shopkeeper only charges for \(12\) chairs (at the discounted rate), so if \(M\) is the marked price, revenue \(=12\times0.78M=9.36M\).
Step 3: Equating revenue to the required \(1638\): \[ 9.36M=1638 \implies M=\frac{1638}{9.36}=175. \]
Final Answer: \[ \boxed{\text{MP} = \text{Rs. }175} \]