Question
The question consists of three statements numbered I, II
and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. What is the cost price of the article (in Rs.)? Statement I: The marked price of the article is Rs. 1,500 more than its selling price. Statement II: Article was marked Rs. 2,100 above its cost price and sold after a discount of 30%. Statement III: Article was marked up by 25% on its cost price and sold at a profit of 10%.Solution
ATQ,
Statement I: Let marked price = Rs. m Selling price = (m – 1,500) But cost price is not connected. → Not sufficient. Statement II: Let cost price = Rs. C Marked price = C + 2,100 Selling price = 0.7(C + 2,100) = 0.7C + 1,470 But cost price can’t be derived. → Not sufficient. Statement III: Let cost price = Rs. C Marked price = 1.25C Selling price = 1.1C But cost price not found directly. → Not sufficient. Statement I and II together: C + 2,100 – (0.7C + 1,470) = 1,500 C + 2,100 – 0.7C – 1,470 = 1,500 0.3C + 630 = 1,500 0.3C = 870 C = 2,900 Therefore, cost price = Rs. 2,900 → Sufficient. Statement II and III together: C + 2,100 = 1.25C 0.25C = 2,100 C = 8,400 Therefore, cost price = Rs. 8,400 → Sufficient. Statement I and III together: 1.25C – 1.1C = 1,500 0.15C = 1,500 C = 10,000 Therefore, cost price = Rs. 10,000 → Sufficient. Hence,, Data given in any two statements combined together is sufficient.
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