On an item, if a company gives a 25% discount, it earns a 25% profit. If it…
2025
On an item, if a company gives a 25% discount, it earns a 25% profit. If it now gives a 10% discount instead, what is the profit percentage?
Answer: C. 50 — Concept: The Selling Price (SP) is obtained by reducing the Marked Price (MP) by the discount percentage, while Profit percentage is always calculated…
- A.
25
- B.
37
- C.
50
- D.
80
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Correct answer: C
Concept: The Selling Price (SP) is obtained by reducing the Marked Price (MP) by the discount percentage, while Profit percentage is always calculated relative to the Cost Price (CP): Profit% = ((SP − CP) / CP) × 100. Since the Cost Price of the item does not change when the discount offered changes, the first scenario (25% discount, 25% profit) can be used to find CP, and that same CP is then used to find the profit for the second scenario (10% discount).
Assume the Marked Price (MP) = 100 (a convenient assumption, since only percentages are involved).
With a 25% discount, the Selling Price is SP1 = 100 − 25 = 75.
This selling price gives a 25% profit, so the Cost Price CP = SP1 / 1.25 = 75 / 1.25 = 60.
With a new discount of 10%, the Selling Price becomes SP2 = 100 − 10 = 90.
The new profit is SP2 − CP = 90 − 60 = 30.
New profit percentage = (Profit / CP) × 100 = (30 / 60) × 100 = 50%.
Cross-check: The discount dropped by 25% − 10% = 15 (in Marked-Price units), so 15 more of the Marked Price flows into profit compared with the first scenario. The original profit was SP1 − CP = 75 − 60 = 15; adding the extra 15 gives the new profit of 15 + 15 = 30, which matches 30/60 × 100 = 50% and confirms the result.