A dealer marks his goods 25% above the cost price and then allows 10% discount on it. What is the cost price of an article on which he gains ₹50 ?
₹400
The dealer marks the goods 25% above cost, then gives 10% discount on the marked price. Work with the cost price (CP) as the base.
Marked Price = CP + 25% of CP = 1.25 × CP.
Selling Price = Marked Price − 10% discount = 1.25 × CP × (1 − 0.10) = 1.25 × 0.90 × CP = 1.125 × CP.
Gain = Selling Price − CP = 1.125 × CP − CP = 0.125 × CP.
We are told the gain is ₹50:
0.125 × CP = 50
CP = 50 / 0.125 = ₹400.
Check: CP ₹400 → marked ₹500 → after 10% discount SP = ₹450 → gain ₹50. Correct.
So the cost price is ₹400. A common trap is treating 25% mark-up and 10% discount as a flat 15% profit, which would wrongly give CP = ₹50 / 0.15 ≈ ₹333; the two percentages act on different bases, so they do not simply subtract. The values ₹350, ₹380 and ₹425 do not yield exactly ₹50 gain.
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