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

Approach: The trap here is "13 chairs for the price of 12" — the shopkeeper bears the cost of all 13 chairs but only collects money for 12 discounted chairs. Equate total SP (built from the 26% profit) with the cash collected, then solve for \(M\).

Step 1: Total cost price. The customer walks away with 13 chairs, so the shopkeeper's cost is on all 13: \[ \text{Total CP} = 13 \times 100 = 1300. \]

Step 2: Total selling price from the profit. A profit of \(26\%\) on cost gives \[ \text{Total SP} = 1300 \times 1.26 = 1638. \]

Step 3: Cash actually collected. Each chair is sold at \(22\%\) off, i.e. \(0.78M\), and money is taken for only \(12\) chairs: \[ \text{Cash} = 12 \times 0.78M = 9.36M. \] This cash is the selling price, so \[ 9.36M = 1638. \]

Step 4: Solve for \(M\). \[ M = \frac{1638}{9.36} = 175. \] Quick check: \(9.36 \times 175 = 1638\), and \(1638/1300 = 1.26\), a clean \(26\%\) profit.

\[ \boxed{M = 175 \text{ rupees}} \]

Answer 2

Approach: Combine the \(22\%\) discount and the "13 for the price of 12" deal into one overall multiplier on the marked price, so the whole problem becomes a single equation.

Step 1: Combine the two effects. The discounted price per chair is \(0.78M\). Giving 13 chairs for the price of 12 means each of the 13 chairs is effectively sold at \(\frac{12}{13}\) of that discounted price. So the true effective price per chair is
\[ 0.78 \times \frac{12}{13} \times M = \frac{9.36}{13}M = 0.72M. \]

Step 2: Use the profit condition. Cost price per chair is Rs 100, and the transaction earns \(26\%\) profit overall (equivalently, per chair, since the deal is uniform), so the effective selling price per chair must be
\[ 100 \times 1.26 = 126. \]

Step 3: Solve for \(M\).
\[ 0.72M = 126 \Rightarrow M = \frac{126}{0.72} = 175. \]

\[ \boxed{\text{Marked price} = \text{Rs } 175} \]