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The following questions have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. A shopkeeper sells two articles for Rs. 1480. Find the amount of overall profit/loss. Statement I: Ratio of loss in 1st article and profit in second article is 3 : 4. Statement II: The shopkeeper sells 1st article at 15% loss and 2nd at 25% profit. Statement III: Cost price of 1st article is equal to the selling price of 2nd article.

The following questions have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. A shopkeeper sells two articles for Rs. 1480. Find the amount of overall profit/loss. Statement I: Ratio of loss in 1st article and profit in second article is 3 : 4. Statement II: The shopkeeper sells 1st article at 15% loss and 2nd at 25% profit. Statement III: Cost price of 1st article is equal to the selling price of 2nd article. Correct Answer Statement II and either Statement I or Statement III are sufficient to answer the question.

Suppose the cost prices of 1st and 2nd item are ‘x’ and ‘y’ respectively;

Statement I and II:

Ratio of loss in 1st article and profit in second article is 3 : 4 (Statement I)

∵ Shopkeeper sells 1st article at 15% loss and 2nd at 25% profit (Statement II)

∴ 0.15x/0.25y = 3/4

⇒ x : y = 5 : 4

And from statement II:

Selling price of 1st article = 0.85x and

Selling price of 2nd article = 1.25y

∵ the shopkeeper sells two articles for Rs. 1480;

∴ 0.85x + 1.25y = 1480

With the help of x : y (= 5 : 4), we can find the values of x and y and thus the overall profit/loss can be determined.

Statement II and III:

∵ Shopkeeper sells 1st article at 15% loss and 2nd at 25% profit (Statement II)

∴ Selling price of 1st article = 0.85x and

Selling price of 2nd article = 1.25y

∵ Cost price of 1st article is equal to the selling price of 2nd article (Statement III)

Selling price of 2nd article = 1.25y = x

∵ the shopkeeper sells two articles for Rs. 1480;

∴ 0.85x + x = 1480

⇒ x = 800

∵ Cost price of 1st article is equal to the selling price of 2nd article (Statement III)

∴ 1.25y = x

Now value of y can be determined and thus the cost prices of both the items will be known.

∴ The overall profit/loss can be determined.

∴ Statement II and either Statement I or Statement III are sufficient to answer the question.

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