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

Approach: Both offers are just price cuts on top of each other. Work with the whole deal of \(13\) chairs: total cost is fixed, profit fixes total revenue, and the "13 for the price of 12" tells you the per-chair selling price after discount.

Step 1 (total CP): CP per chair \(= \)₹\(100\), and \(13\) chairs change hands, so total CP \(= 13 \times 100 = \)₹\(1300\).

Step 2 (total SP from 26% profit): \(\text{Total SP} = 1300 \times 1.26 = \)₹\(1638\).

Step 3 (per-chair selling price): The customer pays for only \(12\) chairs, so each charged chair fetches \[ SP = \frac{1638}{12} = \text{₹}136.5. \]
Step 4 (undo the 22% discount): This ₹\(136.5\) is the discounted price, i.e. \(78\%\) of MP: \[ MP \times 0.78 = 136.5 \Rightarrow MP = \frac{136.5}{0.78} = \text{₹}175. \]
Answer: Marked price of one chair \(= \boxed{\text{₹}175}\).

Answer 2

Approach: Combine the "13 for the price of 12" offer with the 22% discount into one single effective price collected per chair, then use the profit percentage directly.

Let MP \(=M\). The discounted price per chair is \(0.78M\). Selling \(13\) chairs but charging only for \(12\) means the effective price actually collected per chair (spread over all \(13\)) is \[ \frac{12\times0.78M}{13}=\frac{9.36M}{13}. \]
Cost price per chair is Rs. \(100\), and profit is \(26\%\), so the effective selling price per chair must equal \(1.26\times100=126\).

Setting these equal: \[ \frac{9.36M}{13}=126 \implies 9.36M=1638 \implies M=175. \]

So the marked price of a single chair is \[ \boxed{\text{Rs. }175} \]

Answer 3

Concept:

• Instead of working with the whole batch of 13 chairs, reduce everything to what happens for a single chair actually delivered to the customer.
• Out of every 13 chairs handed over, the shopkeeper is only paid for 12 at the discounted rate, so the average revenue collected per chair delivered is a fixed fraction of the discounted price.
• Setting this average revenue per chair equal to CP times (1 + profit fraction) gives a direct equation in MP.

Step 1: Find the discounted selling price per chair.
Let the marked price be $M$. After a $22\%$ discount, the price charged per chair is $0.78M$.

Step 2: Find the average revenue collected per chair delivered.
For every $13$ chairs given to the customer, only $12$ are actually charged for. So the average revenue per chair, spread over all $13$ delivered, is
$\dfrac{12\times0.78M}{13}=\dfrac{9.36M}{13}=0.72M$.

Step 3: Use the profit condition.
CP per chair is Rupees $100$, and profit is $26\%$, so the required average revenue per chair delivered is $100\times1.26=126$.

Step 4: Solve for M.
$0.72M=126 \Rightarrow M=\dfrac{126}{0.72}=175$.

Final Answer: Marked price of one chair $=$ Rupees $175$.