A sweet shop owner buys 10 boxes of sweets for the price of 8 boxes from a wholesaler. If he sells each box at a 2% discount on its marked price, what is his profit percentage?

Correct — C. Take the marked price of one box as ₹100, the wholesaler's price per box.

Cost of 10 boxes = price of 8 = 8 × 100 = ₹800
Cost per box: 800 ÷ 10 = ₹80
Selling price after 2% off: 100 − 2 = ₹98

Profit per box: 98 − 80 = ₹18
Profit %: 18⁄80 × 100 = 22.5% → option (c)

Why the others are wrong

• (a)
  20% — 20% on a cost of ₹80 means selling at ₹96, a 4% discount. The paper gives 2%, so the selling price is ₹98 and the profit ₹18, not ₹16.
• (b)
  24.36% — 24.36% on a cost of ₹80 means selling at about ₹99.49, a discount of roughly 0.5%. A 2% discount brings the price to ₹98, which gives 22.5%.
• (d)
  25.86% — 25.86% on a cost of ₹80 means selling at about ₹100.69, above the ₹100 marked price. Any discount keeps the profit under the 25% of a full-price sale.

Buying 10 for the price of 8 cuts the cost of each box to 8⁄10 of the list price. With the list price at 100, each box costs 80, so a full-price sale earns 20⁄80 = 25%.

The discount comes off the marked price, not the cost. A 2% discount lowers the selling price from 100 to 98, and profit is then measured on the cost of 80: 18⁄80 = 22.5%.

Key facts

• Buying n items for the price of m makes each item cost m⁄n of the list price.
• Profit % = (SP − CP) ⁄ CP × 100, always on the cost price.
• 10 for the price of 8 with no discount gives a profit of 2⁄8 = 25%.

Common traps

• Measuring profit on the ₹100 marked price, 18⁄100 = 18%, instead of on the ₹80 cost.
• Reading the offer as a 2⁄10 = 20% gain, when the 2 free boxes are measured against the 8 paid for.

No directly related past PYQ was found.