A shopkeeper marked an item 25% above its cost price. During a sale, he offered a discount of 10%. What was his profit percentage?

Correct — B. Take the cost price as ₹100.

Marked price = 25% above cost = ₹125
Discount = 10% of ₹125 = ₹12.50
Selling price = ₹125 − ₹12.50 = ₹112.50

Profit = ₹112.50 − ₹100 = ₹12.50 on ₹100 = 12.5% → option (b)

Why the others are wrong

• (a)
  10% — 10% is the discount rate, and ₹12.50 ÷ ₹125 also gives 10% — profit measured on the marked price. Profit % is on the ₹100 cost: 12.5%.
• (c)
  15% — 25 − 10 = 15 subtracts percentages of different bases. The 25% is of cost and the 10% of the marked price, so the discount removes ₹12.50, not ₹10.
• (d)
  17.5% — A 17.5% profit needs a selling price of ₹117.50, only a 6% discount on ₹125. The 10% discount brings the price down to ₹112.50.

A mark-up is a percentage of cost. A discount is a percentage of the marked price. Because the two percentages have different bases, they cannot simply be subtracted.

Chain them as factors instead: 1.25 × 0.90 = 1.125, so the selling price is 112.5% of cost.

The shortcut gives the same: profit % = m − d − (m × d)⁄100 = 25 − 10 − 2.5 = 12.5%.

Key facts

• Mark-up is a percentage of cost price, and discount is a percentage of marked price.
• After a mark-up of m% and a discount of d%, profit % = m − d − (m × d)⁄100.
• A 25% mark-up with a 10% discount leaves the selling price at 112.5% of cost.

Common traps

• Subtracting 25 − 10 = 15% as if both percentages were of cost.
• Dividing the ₹12.50 profit by the ₹125 marked price, which gives 10%, instead of by the ₹100 cost.

No directly related past PYQ was found.