A dealer marks his goods 25% above the cost price and then allows a 10%…
2023
A dealer marks his goods 25% above the cost price and then allows a 10% discount on the marked price. What is the cost price of an article on which he gains ₹50?
Answer: C. ₹400 — CONCEPTWhen an item is marked above cost and then discounted, the percentage factors are applied successively. If the markup rate is m and the discount rate…
- A.
₹350
- B.
₹380
- C.
₹400
- D.
₹425
Show answer & explanation
Correct answer: C
CONCEPT
When an item is marked above cost and then discounted, the percentage factors are applied successively.
If the markup rate is m and the discount rate is d, selling price = cost price × (1 + m) × (1 − d), and profit = selling price − cost price.
APPLICATION
Let the cost price be ₹x. A 25% markup gives marked price = 1.25x.
A 10% discount on the marked price gives selling price = 1.25x × 0.90 = 1.125x.
Hence profit = 1.125x − x = 0.125x. Given profit ₹50, 0.125x = 50, so x = 50 ÷ 0.125 = ₹400.
CROSS-CHECK
For a cost price of ₹400, the marked price is ₹500 and the selling price after a 10% discount is ₹450. The profit is ₹450 − ₹400 = ₹50, matching the condition.
Therefore, the cost price is ₹400.