A merchant marked an article such that its price was 25% above its cost price. He offered two consecutive discounts of 10% and 20% to a buyer. If he incurred a loss of ₹400, what was the marked price of the article?

Correct — A.
Marked price = CP + 25% of CP = 1.25 CP
After 10% off: 0.9 × 1.25 CP = 1.125 CP
After a further 20% off: 0.8 × 1.125 CP = 0.9 CP

Loss = CP − 0.9 CP = 0.1 CP
Set the loss to ₹400: 0.1 CP = 400, so CP = ₹4000

Marked price = 1.25 × 4000 = ₹5000 → option (a).

Why the others are wrong

• (b)
  ₹2000 — ₹2000 gives a loss of ₹160. It means a cost of ₹1600 and a selling price of 0.72 × 2000 = ₹1440. The loss is 10% of cost, so ₹400 needs a cost of ₹4000.
• (c)
  ₹2500 — ₹2500 gives a loss of ₹200. A cost of ₹2000 marked at ₹2500 sells for ₹1800 after both discounts. ₹400 is double that loss, so the marked price must double to ₹5000.
• (d)
  ₹1080 — ₹1080 is far too small to lose ₹400. Marked at ₹1080, the cost is ₹864 and the loss just ₹86.40. A ₹400 loss needs a cost of ₹4000.

Successive discounts of 10% and 20% leave 0.9 × 0.8 = 0.72 of the marked price, a single discount of 28%, not 30%.

With a 25% markup, the selling price is 1.25 × 0.72 = 0.9 of cost: a 10% loss. The ₹400 loss is that 10%, which fixes the cost at ₹4000.

The stem asks for the marked price, so one more step is needed: 1.25 × ₹4000 = ₹5000.

Key facts

• Successive discounts of a% and b% equal one discount of (a + b − ab⁄100)%: 10 + 20 − 2 = 28%.
• SP = 5000 × 0.9 × 0.8 = ₹3600.
• CP = ₹4000, so the loss is 4000 − 3600 = ₹400.

Common traps

• Adding the discounts to a flat 30%: SP = 0.875 CP, a 12.5% loss, which puts the marked price at ₹4000.
• Stopping at the cost price, ₹4000, when the stem asks for the marked price.

No directly related past PYQ was found.