An oven has a marked price of ₹ 12,000. It is sold with two successive discounts. If the second discount is 20% and the final selling price is ₹ 8,400, what is the percentage of the first discount?

Correct — C. Undo the second discount to find the price after the first.

After both discounts: ₹8,400
Undo the 20%: 8,400 ÷ 0.8 = ₹10,500
First discount: 12,000 − 10,500 = ₹1,500

Rate: 1,500 ÷ 12,000 × 100 = 12.5% → option (c)

Why the others are wrong

• (a)
  10% — 10% treats discounts as adding up: 30% overall minus 20%. Applied in turn, 12,000 × 0.9 × 0.8 = ₹8,640, not ₹8,400.
• (b)
  12% — 12% comes close but misses: 12,000 × 0.88 × 0.8 = ₹8,448, which is ₹48 above the final selling price.
• (d)
  15% — 15% overshoots: 12,000 × 0.85 × 0.8 = ₹8,160, which is ₹240 below the final selling price.

Successive discounts multiply, they do not add. Each is taken on the price left by the one before, so the final price is marked price × (1 − d₁⁄100) × (1 − d₂⁄100).

To recover a missing discount, undo the known one by dividing by its factor, not by adding the percentage back. Here 8,400 ÷ 0.8 = 10,500, which is 87.5% of 12,000.

Key facts

• Final price after two successive discounts = marked price × (1 − d₁⁄100) × (1 − d₂⁄100).
• Two successive discounts of d₁% and d₂% equal one discount of (d₁ + d₂ − d₁ × d₂ ÷ 100)%.
• Discounts of 12.5% and 20% in succession equal a single 30% discount.

Common traps

• Subtracting 20% from the 30% overall discount to get 10%. Discounts combine by multiplying, so the first must be 12.5%.
• Undoing the 20% by adding 20% back: 8,400 × 1.2 = 10,080 gives a first discount of 16%. Divide by 0.8 instead.

No directly related past PYQ was found.