After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At…
2025
After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark on his goods?
- A.
28.56%
- B.
35%
- C.
22.22%
- D.
None of these
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Show answer & explanation
Correct answer: A
Solution (exact):
Let cost price = 100. A gain of 14.28% corresponds to 14.28/100 ≈ 1/7, so selling price = 100 × (1 + 1/7) = 800/7 = 114.2857...
An 11.11% discount is 1/9, so the selling price equals (8/9) × marked price. Therefore marked price = selling price × (9/8).
Compute the marked price: (800/7) × (9/8) = 900/7 = 128 4/7. The markup over cost = 900/7 − 100 = 200/7, so the percentage markup = 200/7% = 28 4/7% ≈ 28.5714%.
Answer: 28 4/7% (exact), which is approximately 28.57% (rounded in the options as 28.56%).