An article marked for ₹275 is sold at 5% discount. The seller still gains 4.5%. What did he pay for it?

Correct — A. The 5% discount is reckoned on the marked price, so fix the selling price first.

Discount = 5% of 275 = ₹13.75
SP = 275 − 13.75 = ₹261.25

That selling price carries a gain of 4.5%, and gain is reckoned on cost.
SP = CP × 1.045, so CP = 261.25 / 1.045 = ₹250

Check: 4.5% of 250 is 11.25, and 250 + 11.25 = ₹261.25, the selling price found above → option (a).

Why the others are wrong

• (b)
  ₹200 — ₹200 sold at ₹261.25 is a gain of ₹61.25, which is 30.6%, not 4.5%. No step in the question produces 200.
• (c)
  ₹225 — ₹225 gives a gain of ₹36.25 on the same selling price, about 16.1%. For 4.5% to hold on a cost of ₹225 the marked price would have to be ₹247.50, not ₹275.
• (d)
  ₹125 — ₹125 is half the correct cost and would mean a gain of 109% on a selling price of ₹261.25. Nothing in the question halves the cost price.

Discount is always a percentage of the marked price; profit is always a percentage of the cost price. Mixing the two bases is the standard error in this topic.

The selling price is the hinge that joins them: MP − discount = SP, and SP = CP × (1 + gain).

So move in one direction only. Get SP from MP, then divide by 1.045 to recover CP. Dividing by 1.045 is not the same as subtracting 4.5%, which would give about ₹249.49 and no option.

Key facts

• Discount is a percentage of the marked price, while profit is a percentage of the cost price.
• SP = 275 × 0.95 = ₹261.25 and CP = 261.25 / 1.045 = ₹250.
• One relation carries the whole question: CP × 1.045 = MP × 0.95.
• At MP = ₹275 and CP = ₹250 the ratio CP : MP is 10 : 11.

Common traps

• Subtracting 4.5% from the selling price instead of dividing by 1.045
• Taking the 4.5% gain on the marked price rather than on the cost price
• Stopping at the selling price of ₹261.25, which the question never asks for

No directly related past PYQ was found.