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?
₹12,000
Track the price through each stage as a multiplier on the base cost C.
Step 1 — Wholesaler's price (50% markup):
\(P_1 = 1.50\,C\)
Step 2 — Retailer's cost (after 20% trade discount on \(P_1\)):
\(P_2 = 1.50\,C \times 0.80 = 1.20\,C\)
Step 3 — Printed (marked) price after retailer's 40% markup on his cost:
\(P_3 = 1.20\,C \times 1.40 = 1.68\,C\)
Step 4 — Customer's price after 10% discount on printed price:
\(P_4 = 1.68\,C \times 0.90 = 1.512\,C\)
Step 5 — Solve:
\(1.512\,C = 18144 \implies C = \dfrac{18144}{1.512} = \mathbf{₹12{,}000}\)
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