A wholesaler buys a batch of ceiling fans at a 50% markup over the factory's base cost ₹C. He then allows a 20% trade discount to the retailer. The retailer applies a 40% markup on his cost and offers a flat 10% discount to customers on the printed price. If a customer finally pays ₹18,144, what is the original base cost (₹C) of one ceiling fan from the factory?

Correct — A. Each step multiplies the price, so chain the four multipliers on C.

50% markup: C × 1.5 = 1.5C
20% trade discount: 1.5C × 0.8 = 1.2C (retailer's cost)
40% markup: 1.2C × 1.4 = 1.68C (printed price)

10% discount: 1.68C × 0.9 = 1.512C
1.512C = 18,144
C = 18,144 ÷ 1.512 = ₹12,000 → option (a)

Why the others are wrong

• (b)
  ₹11,500 — Run it forward: 11,500 × 1.512 = ₹17,388, which is ₹756 short of the ₹18,144 the customer pays.
• (c)
  ₹10,800 — 10,800 × 1.512 = ₹16,329.60, exactly 10% below the ₹18,144 paid, because ₹10,800 is 90% of ₹12,000.
• (d)
  ₹10,000 — 10,000 × 1.512 = ₹15,120, which is ₹3,024 short of the ₹18,144 the customer pays.

A markup of m% multiplies a price by (1 + m⁄100) and a discount of d% by (1 − d⁄100). Successive changes therefore multiply; they never add.

Here 1.5 × 0.8 × 1.4 × 0.9 = 1.512, so the customer pays 51.2% more than the factory's base cost. To get back to C, divide the final price by the whole product in one step.

Key facts

• Markup of m%: multiply by (1 + m⁄100). Discount of d%: multiply by (1 − d⁄100).
• 1.5 × 0.8 × 1.4 × 0.9 = 1.512.
• The order of successive percentage changes does not affect the final multiplier.
• 12,000 × 1.512 = 18,144.

Common traps

• Adding the percentages: +50 − 20 + 40 − 10 = +60% gives C = 18,144 ÷ 1.6 = ₹11,340, not an option.
• Stopping after the first step back: 18,144 ÷ 0.9 = ₹20,160 is the retailer's printed price, not C.

No directly related past PYQ was found.