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Abhishek ordered 6 pair of red shoes and some pair of books. The price of a pair of red shoes is double than that of a pair of book. While preparing the bill the shopkeeper interchanged the number of pair of shoes and books by mistake which increased the bill by 40%. What was the ratio of the number of pair of red shoes and the number of pair of books in the original order?

Abhishek ordered 6 pair of red shoes and some pair of books. The price of a pair of red shoes is double than that of a pair of book. While preparing the bill the shopkeeper interchanged the number of pair of shoes and books by mistake which increased the bill by 40%. What was the ratio of the number of pair of red shoes and the number of pair of books in the original order? Correct Answer 1 : 3

Given :

Abhishek ordered 6 pair of red shoes and some pair of books

Formula used :

Total bill = Number of pair of red shoes × Price of a pair of red shoes + Number of pair of book × Price of a pair of a book

Calculation :

Let the number of pair of books be x.

Price of pair of red shoes : Price of pair of book = 2y : y

For first condition,

Total bill = Number of pair of red shoes × Price of pair of red shoes + Number of pair of book × Price of pair of book

⇒ Total bill = 6 × 2y + xy

⇒ Total bill = y(12 + x)

For second condition,

The shopkeeper interchanged the number of pair of shoes and pair of books by mistake.

Total bill = Number of pair of red shoes × Price of pair of red shoes + Number of pair of book × Price of pair of book

⇒ Total bill = x × 2y + 6y

⇒ Total bill = 2xy + 6y

According to question:

140% × (12 + x)y = 2y(x + 3)

⇒ 84 + 7x = 10x + 30

⇒ 3x = 54

⇒ x = 18

∴ The ratio of the number of pair of red shoes and the number of pair of books in the original order = 6 : x = 6 : 18 = 1 : 3

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