A furniture store marks its items at 80% above the cost price. They offer a discount of 30% on the marked price. If a customer receives an additional loyalty discount of ₹250, and the store still makes a 12% profit on the cost price, what is the cost price of the furniture item?

Correct — A. Let the cost price be x.

Mark up 80%: marked price = 1.8x
Discount 30%: 0.7 × 1.8x = 1.26x
Loyalty discount: selling price = 1.26x − 250

12% profit: selling price = 1.12x
Equate: 1.26x − 250 = 1.12x
Subtract 1.12x: 0.14x = 250

Divide: x = 250 ÷ 0.14 = 1,785.714…
Cost price ≈ ₹1,785.71 → option (a)

Why the others are wrong

• (b)
  ₹2,585.36 — 0.14 × 2,585.36 ≈ 361.95, but the gap between the discounted price (1.26x) and the selling price (1.12x) has to be the ₹250 loyalty discount.
• (c)
  ₹1,528.24 — 0.14 × 1,528.24 ≈ 213.95, short of ₹250. At this cost the 12% profit would survive a loyalty discount of about ₹214, not ₹250.
• (d)
  ₹2,879.45 — 0.14 × 2,879.45 ≈ 403.12. A cost this high could absorb a ₹403 loyalty discount and still earn 12%, so the stem's ₹250 points to a smaller cost.

Chain the percentage steps as multipliers on the cost. An 80% markup is × 1.8 and a 30% discount is × 0.7, so the price before the loyalty discount is 1.26 times cost: a 26% margin.

A flat rupee discount is subtracted, not multiplied in, and it eats that margin. 26% of cost minus ₹250 must leave exactly 12% of cost, so 14% of the cost price is ₹250.

Key facts

• An 80% markup followed by a 30% discount: 1.8 × 0.7 = 1.26, a net 26% above cost.
• A flat rupee discount is subtracted after the percentage steps.
• The selling price here comes to exactly ₹2,000.

Common traps

• Netting 80% − 30% = 50% instead of multiplying 1.8 × 0.7 = 1.26.
• Taking the 30% off the cost price rather than off the marked price.

No directly related past PYQ was found.