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.?

Option 2 : Statement II and either Statement I or Statement III are sufficient to answer the question.

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

Statement I and II:

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

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

∴ 0.15x/0.25y = 3/4

⇒ x : y = 5 : 4

And from statement II:

Selling price of 1^st article = 0.85x and

Selling price of 2^nd 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 1^st article at 15% loss and 2^nd at 25% profit (Statement II)

∴ Selling price of 1^st article = 0.85x and

Selling price of 2^nd article = 1.25y

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

Selling price of 2^nd article = 1.25y = x

∵ the shopkeeper sells two articles for Rs. 1480;

∴ 0.85x + x = 1480

⇒ x = 800

∵ Cost price of 1^st article is equal to the selling price of 2^nd 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.