A shopkeeper marked an item 50% above its cost price. He then offered two successive discounts of 10% and 20% to a customer. If he made a profit of ₹80, at what price did he sell the item to that customer?

Correct — C.
Take the cost price as ₹x.
Mark up 50%: marked price = 1.5x
First discount 10%: 1.5x × 0.9 = 1.35x

Second discount 20%: 1.35x × 0.8 = 1.08x
Profit: 1.08x − x = 0.08x = ₹80, so x = ₹1000
Selling price: 1.08 × 1000 = ₹1080 → option (c)

Why the others are wrong

• (a)
  ₹2000 — ₹2000 as the selling price would mean a cost of 2000 ÷ 1.08 ≈ ₹1852 and a profit of about ₹148, not the ₹80 stated.
• (b)
  ₹2500 — ₹2500 as the selling price would mean a cost of 2500 ÷ 1.08 ≈ ₹2315 and a profit of about ₹185, far above ₹80.
• (d)
  ₹1000 — ₹1000 is the cost price, the value of x. The question asks what the customer paid, which is 8% more than cost: ₹1080.

Turn every percentage change into a multiplier on the cost price. A 50% mark-up is × 1.5, a 10% discount is × 0.9, a 20% discount is × 0.8.

Multiply them: 1.5 × 0.9 × 0.8 = 1.08. The item sells at 108% of cost, so the ₹80 profit is 8% of cost. That fixes the cost at ₹1000 and the sale at ₹1080.

Key facts

• Successive discounts of 10% and 20% multiply: 0.9 × 0.8 = 0.72, a net cut of 28%, not 30%.
• A 50% mark-up followed by the 0.72 factor: 1.5 × 0.72 = 1.08, a profit of 8% on cost.
• Profit in rupees ÷ profit as a fraction of cost = cost price: 80 ÷ 0.08 = ₹1000.

Common traps

• Adding the discounts to 30%: 1.5 × 0.7 = 1.05 gives a 5% profit and a wrong cost of ₹1600
• Stopping at x = ₹1000 and marking the cost price instead of the selling price

No directly related past PYQ was found.