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:

In problems with multiple discounts (e.g., percentage discount plus a quantity offer like 'buy X, pay for Y'), always calculate the total cost of all items given to the customer and the total money received. This simplifies finding the effective profit or loss.

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: \[ \boxed{\text{MP} = \text{Rs. }175} \]