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?
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Correct Answer: 175
Solution and Explanation
Step 1: Understanding the Question
A shopkeeper sells chairs using two offers:
- A 22% discount on the marked price
- A Buy 12 Get 1 Free offer (13 chairs given, payment for 12)
Even after these offers, the shopkeeper makes a 26% profit. The cost price (CP) of one chair is ₹100. We need to find the marked price (MP) of one chair.
Step 2: Key Formulae Used
- Total Selling Price:
\( SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \) - Discount Formula:
\( SP = MP \times \left(1 - \frac{\text{Discount \%}}{100}\right) \)
Step 3: Detailed Solution
Part A: Total Cost Price
Cost price of 1 chair = ₹100
Total chairs given = 13
\[ \text{Total CP} = 13 \times 100 = ₹1300 \]
Part B: Total Selling Price
Profit = 26% of 1300
\[ \text{Profit} = \frac{26}{100} \times 1300 = ₹338 \] \[ \text{Total SP} = 1300 + 338 = ₹1638 \]
Part C: Effective Selling Price Per Chair
Customer pays for only 12 chairs but receives 13.
\[ 12 \times SP_{\text{eff}} = 1638 \] \[ SP_{\text{eff}} = \frac{1638}{12} = ₹136.5 \]
Part D: Calculate Marked Price
Discount = 22%
\[ 136.5 = MP \times \left(1 - \frac{22}{100}\right) \] \[ 136.5 = MP \times 0.78 \] \[ MP = \frac{136.5}{0.78} = ₹175 \]
Step 4: Final Answer
The marked price of one chair is ₹175.
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