A trader offers a discount of 26% on an article if a customer makes the…
2026
A trader offers a discount of 26% on an article if a customer makes the payment in cash. What percentage above the cost price should he mark the article to make a profit of 26%? [Answer rounded off to 2 decimal places]
Answer: D. 70.27% — ConceptWhen an article is marked x% above cost price, its marked price is CP × (1 + x/100). After a discount of d%, the selling price is MP × (1 − d/100). A…
- A.
68.79%
- B.
72.26%
- C.
66.03%
- D.
70.27%
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Show answer & explanation
Correct answer: D
Concept
When an article is marked x% above cost price, its marked price is CP × (1 + x/100). After a discount of d%, the selling price is MP × (1 − d/100).
A profit of p% means SP = CP × (1 + p/100). Equating the two expressions for selling price determines the required markup.
Application
Let the cost price be ₹100. A profit of 26% requires the selling price to be ₹126.
A 26% discount means the customer pays 74% of the marked price, so 0.74 × MP = 126.
Therefore, MP = 126 ÷ 0.74 = ₹170.27027… .
Required markup = [(170.27027… − 100) ÷ 100] × 100% = 70.27027…%.
Cross-check
Applying the 26% discount to ₹170.27027… gives ₹170.27027… × 0.74 = ₹126, which is exactly 26% above the ₹100 cost price.
Rounded to two decimal places, the required markup is 70.27%.