The profit made on an item sold for ₹2200 is equal to the loss incurred when it is sold for ₹1800. What will be the profit or loss percentage if the item is sold for ₹2050?

Correct — C. Let the cost price be C.

Profit at ₹2200 = 2200 − C
Loss at ₹1800 = C − 1800
Set them equal: 2200 − C = C − 1800 → 2C = 4000 → C = ₹2000

At ₹2050: profit = 2050 − 2000 = ₹50
Profit % = 50 ÷ 2000 × 100 = 2.5% → option (c)

Why the others are wrong

• (a)
  Profit of 2.25% — A 2.25% profit on ₹2000 is ₹45, a selling price of ₹2045. The item sells for ₹2050, ₹50 above cost, which is 2.5%.
• (b)
  Loss of 3.5% — ₹2050 is above the ₹2000 cost, so this sale makes a profit and no loss is possible. A 3.5% loss would mean selling at ₹1930.
• (d)
  Loss of 4.25% — A 4.25% loss would mean selling at ₹1915, below cost. At ₹2050 the seller is ₹50 above his ₹2000 cost, so the result is a profit.

Profit and loss are both measured from the cost price. If the profit at one price equals the loss at another, the cost price sits exactly halfway between them.

Here that midpoint is (2200 + 1800) ÷ 2 = ₹2000, and each price is ₹200 away from it.

Once the cost is known, any new selling price gives the profit or loss directly, and the percentage is taken on cost.

Key facts

• Equal profit at S₁ and loss at S₂ means cost price = (S₁ + S₂) ÷ 2.
• Profit % = profit ÷ cost price × 100.
• A selling price above cost gives a profit, and one below cost gives a loss.

Common traps

• Taking the ₹50 profit as a share of the selling price: 50 ÷ 2050 ≈ 2.44%, but profit % is on cost.
• Comparing ₹2050 with ₹2200 and expecting a loss: the comparison that matters is with the ₹2000 cost.

No directly related past PYQ was found.