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The ratio of the cost prices of articles A, B, and C is 8:5:3. The percentage by which articles A, B, and C are marked up is 80%, 60%, and 40% respectively. Statement I: The ratio of the selling prices of articles A, B, and C is 10:7:13. Statement II: The total profit earned on the three articles is ₹120 less than the total discount given on the three articles together. Question: Find the cost price of article C.
- The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
- The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
- The data either in statement I alone or in statement II alone are sufficient to answer the question.
- The data given in both statements I and II together are not sufficient to answer the question.
Correct answer: The data given in both statements I and II together are not sufficient to answer the question.
Solution
The given markup percentages let us write selling prices as multiples of the cost prices, but they do not by themselves determine the absolute cost prices. Statement I gives only a ratio of selling prices, and Statement II gives only a relation between total profit and total discount; neither fixes the actual value of C. Even together, they still do not uniquely determine the scale of the cost-price ratio, so the cost price of C cannot be found exactly.
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