A man sells an article at a profit of 25%. If he had bought it at 20% less and…
2024
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 10.50 less, he would have gained 30%. Find the cost price (in rupees) of the article?
- A.
50
- B.
20
- C.
25
- D.
35
Show answer & explanation
Correct answer: A
Concept: For an article bought at cost price CP and sold at a profit of p%, the selling price is SP = CP × (1 + p/100). When the cost price changes by a fixed percentage and the profit percentage also changes, express both selling prices in terms of the original cost price and equate the given difference to solve for CP.
Application:
Let the original cost price be x.
First selling price (25% profit) = 1.25x.
New cost price (20% less) = 0.8x.
New selling price (30% profit on the new cost) = 1.3 × 0.8x = 1.04x.
The new selling price is Rs 10.50 less than the first: 1.25x − 1.04x = 10.50.
Simplify: 0.21x = 10.50.
Solve: x = 10.50 ÷ 0.21 = 50.
Cross-check: With x = 50, the first selling price is 62.5, the new cost price is 40, and the new selling price at 30% profit is 52; the difference 62.5 − 52 = 10.5 confirms the cost price is Rs 50.