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A retailer marks an air conditioner 80% above its cost price

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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?

एक दुकानदार एयर कंडीशनर का अंकित मूल्य उसके क्रय मूल्य से 80% अधिक रखता है। वह पहले अंकित मूल्य पर 25% की छूट देता है। त्योहारी ऑफर में पहले से छूट वाले मूल्य पर अतिरिक्त 10% की छूट दी जाती है। यदि अंतिम विक्रय मूल्य ₹15,552 है, तो एयर कंडीशनर का लगभग क्रय मूल्य ज्ञात कीजिए।

Options / विकल्प

A. ₹9,000

B. ₹9,200

C. ₹12,800 ✅

D. ₹10,000

Answer / उत्तर

✅ ₹12,800

Solution / समाधान

Shortcut Trick / शॉर्टकट ट्रिक

Let the Cost Price be CP.

क्रय मूल्य = CP मान लेते हैं।

Marked Price (MP)

MP=CP×(1+80100)MP = CP \times \left(1+\frac{80}{100}\right)
MP=CP×180100MP = CP \times \frac{180}{100} MP=CP×95MP = CP \times \frac{9}{5}

After 25% discount

MP×75100=CP×95×34MP \times \frac{75}{100} = CP \times \frac{9}{5}\times\frac{3}{4}

After additional 10% discount

SP=CP×95×34×910SP = CP \times \frac{9}{5}\times\frac{3}{4}\times\frac{9}{10} SP=CP×243200SP = CP \times \frac{243}{200}

Given,

SP=₹15,552SP = ₹15,552 15,552=CP×24320015,552 = CP \times \frac{243}{200} CP=15,552×200243CP = 15,552 \times \frac{200}{243} CP=₹12,800CP = ₹12,800

Quick Method / त्वरित विधि

Successive discounts:

75%×90%=67.5%75\% \times 90\% = 67.5\%

Thus,

SP=180%×67.5%=121.5% of CPSP = 180\% \times 67.5\% = 121.5\% \text{ of CP}
CP=15,5521.215=₹12,800CP = \frac{15,552}{1.215} = ₹12,800

Final Answer / अंतिम उत्तर

₹12,800\boxed{₹12,800}

✅ Correct Answer / सही उत्तर: ₹12,800

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