An article is marked at ₹550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in ₹)?

Correct — C. Bring the marked price down first, then read the selling price against cost.

Discount 40% on ₹550: SP = 550 × 60⁄100 = ₹330
SP is 10% above CP, so SP = 1.1 × CP

CP = 330 ⁄ 1.1 = ₹300 → option (c)
Check: 10% of 300 is 30, and 300 + 30 = ₹330.

Why the others are wrong

• (a)
  330 — ₹330 is the selling price, the number the first step produces. Stop there and you have answered a question the paper did not ask — cost price is still one division away.
• (b)
  220 — ₹220 is the discount itself, 40% of ₹550. Treat it as cost and the selling price would be 220 × 1.1 = ₹242, not the ₹330 the discount actually leaves.
• (d)
  200 — ₹200 would put the selling price 65% above cost, since 330 ⁄ 200 = 1.65. The stem allows only 10%, so ₹200 is far too low.

Marked price, selling price and cost price are three separate figures, and each percentage names its own base.

A discount is always on the marked price: SP = M × (100 − d)⁄100. A profit is always on the cost price: SP = CP × (100 + p)⁄100.

This item chains the two. The discount converts ₹550 into ₹330, then the profit relation converts ₹330 back into ₹300.

Key facts

• Selling price after a discount d on marked price M is SP = M × (100 − d)⁄100.
• 'SP is 10% more than CP' means SP = 1.1 × CP, so CP = SP ⁄ 1.1.
• Here SP = ₹330 and CP = ₹300, a profit of ₹30 on a ₹550 tag.

Common traps

• Answering ₹330, the selling price, because it is the first number the working produces
• Computing CP as 330 × 0.9 = ₹297 instead of 330 ⁄ 1.1 = ₹300
• Applying the 40% discount to the cost price rather than to the marked price

No directly related past PYQ was found.