A retailer marks an air conditioner 80% above its cost price. He offers a first discount of 25% on the marked price. During a fes…

Question

A retailer marks an air conditioner 80% above its cost price. He offers a first discount of 25% on the marked price. During a festive offer, an additional discount of 10% is applied on the already discounted price. If the final selling price is ₹15,552, what is the approximate cost price of the air conditioner?

1. A. ₹9,000
2. B. ₹9,200
3. C. ₹12,800 (Correct answer)
4. D. ₹10,000

Correct Answer

Option C — ₹12,800

Detailed Solution & Explanation

The correct answer is ₹12,800.

Key Points

• Let CP = x. Mark-up 80% → MP = 1.8x.
• First discount 25% → 1.8x × 0.75 = 1.35x.
• Festive discount 10% → 1.35x × 0.90 = 1.215x.
• Set equal to the final price: 1.215x = 15,552 → x = 15,552 / 1.215 = ₹12,800.
• Apply successive discounts multiplicatively (0.75 then 0.90), never by adding them, then divide the final price by the combined factor.