Profit and Loss Question 3 - CAT 2025
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:
Step-by-Step Explanation
- Cost Price (CP) for the shopkeeper:
The customer gets 13 chairs. Since each chair costs Rs. 100, the total cost price incurred by the shopkeeper is:
Total CP = 13 × 100 = Rs. 1300
- Selling Price (SP) earned by the shopkeeper:
The shopkeeper makes a 26% profit on the entire transaction.
Total Revenue (SP) = 1300 × 1.26 = Rs. 1638
- Connecting to Marked Price (MP):
The customer only pays the discounted price for 12 chairs to generate this total revenue.
Discounted SP per chair = 1638 / 12 = Rs. 136.5
Each chair is sold at a 22% discount on its marked price (MP):
MP × (1 − 0.22) = 136.5
0.78 × MP = 136.5
MP = 136.5 / 0.78 = 175
The marked price of each chair is Rs. 175.
Correct Answer: 175
💡 FundaMakers Tip:
Don't let "Buy X get Y free" offers confuse you. Always evaluate the transaction from the shopkeeper's macro perspective:
- Total Outflow (CP): How many units left the store? (13 chairs)
- Total Inflow (Revenue): How many units did the customer actually pay for? (12 chairs)
Focus on the net cash flow first, and then break it down to a single unit's pricing structure at the very end.