Multiple choice

In a bookstore, the average price of books sold increased by Rs. 10 when a new collection of books was added. The average price of the new collection of books is Rs. 80 more than half the average price of the original books. If the ratio of the number of original books to the number of books from new collection is 3 : 2, what is the average price of the new collection of books?

  1. 55

  2. 80

  3. 135

  4. 155

  5. a
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C Correct answer
Explanation

Let original average = x. Original books = 3k, new books = 2k. Total books = 5k. New average = x + 10. New collection average = 0.5x + 80. Equation: (3k*x + 2k*(0.5x + 80)) / 5k = x + 10. (3x + x + 160) / 5 = x + 10. 4x + 160 = 5x + 50. x = 110. New collection average = 0.5(110) + 80 = 55 + 80 = 135.

AI explanation

Let the average price of the original books be P. According to the given ratio, there are 3 original books and 2 new books, making a total of 5 books. The new average price is P plus 10, and the average price of the new collection is P divided by 2 plus 80. The equation becomes 3 times P plus 2 times the quantity P divided by 2 plus 80, all divided by 5, equals P plus 10. Solving this equation, 3P plus P plus 160 equals 5P plus 50, results in P being 110. The average price of the new collection is 110 divided by 2 plus 80, which equals 135.

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