A trader buys 12 fans for ₹ 24,000. He marks each fan at 25% above the cost…
2024
A trader buys 12 fans for ₹ 24,000. He marks each fan at 25% above the cost price. If he sells all fans by giving 10% discount on the marked price, then his overall profit (in ₹) is :
- A.
2700
- B.
3000
- C.
3200
- D.
3500
Show answer & explanation
Correct answer: B
Concept: When a cost price (CP) is marked up by x% to get the marked price (MP), and then a discount of y% is applied on the MP to get the selling price (SP), the net change in price is NOT simply (x − y)%. The exact relation is SP = CP × (1 + x/100) × (1 − y/100), and profit equals total selling price minus total cost price.
Cost price per fan = ₹24,000 ÷ 12 = ₹2,000.
Marked price per fan = CP + 25% of CP = ₹2,000 × 1.25 = ₹2,500.
Selling price per fan = MP − 10% of MP = ₹2,500 × 0.9 = ₹2,250.
Total selling price for all 12 fans = ₹2,250 × 12 = ₹27,000.
Overall profit = Total SP − Total CP = ₹27,000 − ₹24,000 = ₹3,000.
Cross-check: Using the successive-percentage-change shortcut, a 25% markup followed by a 10% discount gives a net change of 25 + (−10) + (25 × −10)/100 = 12.5% on the cost price. 12.5% of ₹24,000 = ₹3,000, confirming the step-by-step total.