A wholesaler buys a batch of ceiling fans at a 60% markup over the factory's base cost C. He then allows a 25% trade discount to the retailer. The retailer applies a 30% markup on his cost and offers a flat 15% discount to customers on the printed price. If a customer finally pays ₹20,400, what is the original base cost (C) of one ceiling fan from the factory?
Show answer & explanation
Correct answer: A
Explanation
Original base cost (C) ≈ ₹15,384.62
Working:
Step 1: Wholesaler's cost to retailer
Wholesaler buys at 60% markup over C:
Wholesaler's price = 1.6C
Wholesaler gives 25% trade discount to retailer:
Retailer's cost = 1.6C × 0.75 = 1.2C
Step 2: Retailer's printed price
Retailer applies 30% markup on his cost (1.2C):
Printed price = 1.2C × 1.30 = 1.56C
Step 3: Final price after discount
Retailer offers 15% discount on printed price:
Final price = 1.56C × 0.85 = 1.326C
Step 4: Solve for C
1.326C = 20400
C = 20400/1.326
C ≈ ₹15,384.62
Verification:
Wholesaler's price = 1.6 × 15384.62 = ₹24,615.38
Retailer's cost (after 25% discount) = 24615.38 × 0.75 = ₹18,461.54
Printed price (after 30% markup) = 18461.54 × 1.30 = ₹24,000
Final price (after 15% discount) = 24,000 × 0.85 = ₹20,400 ✓
C ≈ ₹15,384.62