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?
₹500
Let the cost price be \(CP\).
Step 1 — marked price after a 40% mark-up:
\(MP = CP \times \left(1+\dfrac{40}{100}\right) = 1.4\, CP\)
Step 2 — selling price after a 20% discount on MP:
\(SP = MP \times \left(1-\dfrac{20}{100}\right) = 0.8 \times 1.4\, CP = 1.12\, CP\)
Step 3 — equate to the given SP and solve:
\(1.12\, CP = 560 \;\Longrightarrow\; CP = \dfrac{560}{1.12} = 500\)
Hence the cost price is ₹500 — option (1).
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