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?"

Correct — C. Turn every step into a multiplier on the cost price and chain them.

Mark-up 80%: MP = 1.8 × CP
First discount 25%: 1.8 × 0.75 = 1.35 × CP
Second discount 10%: 1.35 × 0.9 = 1.215 × CP

1.215 × CP = 15,552
CP = 15,552 ÷ 1.215 = ₹12,800 → option (c).

Why the others are wrong

• (a)
  ₹9,000 — Run it forward: 9,000 × 1.8 × 0.75 × 0.9 = ₹10,935, about ₹4,600 short of the ₹15,552 selling price.
• (b)
  ₹9,200 — Forward check: 9,200 × 1.215 = ₹11,178. The stem's selling price is ₹15,552, so this cost is far too low.
• (d)
  ₹10,000 — Forward check: 10,000 × 1.215 = ₹12,150, not ₹15,552. A cost of ₹10,000 would need a final price about ₹3,400 lower than the one given.

Successive percentage changes multiply; they do not add. An 80% mark-up and discounts of 25% and 10% give 1.8 × 0.75 × 0.9 = 1.215, a net 21.5% above cost.

Once the net multiplier is known, the cost price is one division: SP ÷ 1.215.

The second discount is on the already discounted price, so 25% then 10% is a single discount of 32.5%, not 35%.

Key facts

• Successive discounts of a% and b% leave (1 − a⁄100)(1 − b⁄100) of the marked price.
• Discounts of 25% then 10% equal a single discount of 32.5%.
• An 80% mark-up followed by 25% and 10% discounts sells at 1.215 times cost, a 21.5% profit.

Common traps

• Adding the discounts to 35%, which gives 1.8 × 0.65 = 1.17 and a cost of about ₹13,292.
• Netting everything as 80 − 25 − 10 = 45% profit, which gives 15,552 ÷ 1.45 ≈ ₹10,726.

No directly related past PYQ was found.