If the cost price of 8 pens is same as the selling price of 6 pens, then the…
2018
If the cost price of 8 pens is same as the selling price of 6 pens, then the gain percent is
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When the cost price of a larger number of articles equals the selling price of a smaller number of the same articles, a gain results. In general, if the cost price of m articles equals the selling price of n articles (m > n), then (selling price per article) : (cost price per article) = m : n, and gain % = [(m − n) / n] × 100.
Let the cost price of 1 pen be C and the selling price of 1 pen be S.
Given: cost price of 8 pens = selling price of 6 pens, so 8C = 6S.
Solving for S: S = (86)C = (43)C.
Gain per pen = S − C = (43)C − C = (13)C.
Gain % = (Gain per pen ÷ C) × 100 = (13) × 100 = 33 13%.
Cross-check with real numbers: take C = 3, so the cost price of 8 pens = 24. Then S = 4, since the selling price of 6 pens (6 × 4 = 24) equals that same 24. Gain per pen = 4 − 3 = 1, and gain % = (13) × 100 = 33 13%, confirming the result.