A trader marked an article 40% above its cost price. He then allowed a discount of 20% on the marked price. If the selling price of the article was ₹560, what was its cost price?

Correct — A.
Let the cost price be C.

Mark up 40%: MP = 1.4 × C
Allow 20% off: SP = 0.8 × 1.4 × C = 1.12 × C

Set SP = 560: 1.12 × C = 560
Divide: C = 560 ÷ 1.12 = ₹500 → option (a)

Check: MP = ₹700, 20% of 700 = ₹140, 700 − 140 = ₹560.

Why the others are wrong

• (b)
  ₹209 — ₹209 × 1.12 = ₹234.08, less than half the stated selling price of ₹560.
• (c)
  ₹306 — ₹306 × 1.12 = ₹342.72. A 40% mark-up followed by 20% off must land on ₹560, and this falls far short.
• (d)
  ₹456 — ₹456 × 1.12 = ₹510.72, close but still ₹49.28 below ₹560.

Successive percentage changes multiply; they do not add. A 40% mark-up multiplies the cost by 1.4, a 20% discount multiplies the marked price by 0.8, and the net factor is 1.4 × 0.8 = 1.12, a 12% profit.

The formula a + b + ab⁄100 gives the same figure: 40 − 20 − 800⁄100 = 12%.

With the net factor known, divide the selling price by it to get back to the cost.

Key facts

• Mark-up of m% then discount of d%: SP = CP × (1 + m⁄100) × (1 − d⁄100)
• 40% up then 20% off is a net 12% gain, not 20%
• 560 ÷ 1.12 = 500

Common traps

• Netting 40% − 20% = 20% and dividing 560 by 1.2, which gives ₹466.67
• Taking the 20% discount on the cost price instead of the marked price

No directly related past PYQ was found.