The marked price of an article is 26% more than its cost price. If a discount of 32% is given, what will be the loss percentage?

Correct — D. Every figure here is a percentage, so set CP = 100.

MP is 26% above cost: MP = 126
A 32% discount leaves 68% of MP: SP = 126 × 0.68 = 85.68
SP is below cost, so it is a loss: 100 − 85.68 = 14.32
Loss on a cost of 100 = 14.32% → option (d).

In one shot: SP = CP × 1.26 × 0.68 = 0.8568 × CP.

Why the others are wrong

• (a)
  12.26% — A 12.26% loss puts SP at 87.74, which is 87.74 ÷ 126 of the marked price — a discount of about 30.4%, not the 32% the stem fixes.
• (b)
  15.25% — A 15.25% loss puts SP at 84.75, a discount of roughly 32.7% on the marked price of 126. Close, but the stem gives exactly 32%.
• (c)
  18.64% — An 18.64% loss needs SP = 81.36, a discount of about 35.4% on 126. Overshooting like this usually means the 32% was applied to the cost price.

Markup and discount are percentages of different bases: the markup sits on cost price, the discount on marked price. They can never simply be subtracted from each other.

Fixing CP = 100 turns the whole chain into one product, SP = CP × (1 + markup) × (1 − discount), and the profit or loss percentage is then read straight off a base of 100.

Whenever that product is less than 1 the trade is a loss of (1 − product) × 100 percent — check the direction before you compute anything.

Key facts

• SP = CP × (1 + markup%) × (1 − discount%).
• Here 1.26 × 0.68 = 0.8568, so SP is 85.68% of cost.
• A 26% markup with a 32% discount always loses, because 1.26 × 0.68 is less than 1.
• With CP = 100 the markup is 26 and the discount 40.32.
• The 14.32 loss is exactly that discount minus that markup, 40.32 − 26.

Common traps

• Subtracting the percentages, 32 − 26, and answering a 6% loss
• Applying the 32% discount to the cost price instead of the marked price
• Reporting the loss on the selling price: 14.32 ÷ 85.68 = 16.71%

No directly related past PYQ was found.