Question
Peter had some books in his library. He tried packing them in bags in various ways. While packing 85 books in each bag, 9 bags were not filled completely. Also, while packing 58 books in each bag, 13 bags were not enough to pack all the books. But in the end, he was able to pack the books in M bags, each having M books. How many books did Peter have?
- 765
- 812
- 729
- 784
Hint:
Total books = M × M = M2.
The correct answer is: 784
GIVEN-
While packing 85 books in each bag, 9 bags were not filled completely.
While packing 58 books in each bag, 13 bags were not enough to pack all the books.
Final arrangement- M bags, each having M books.
TO FIND-
Total number of books peter had.
SOLUTION-
Since M bags are there and each has M books,
Total books = M × M = M2.
From the given options, only 729 (272) and 784 (282) are perfect squares.
The second condition is that with 58 books in each bag, 13 bags are not sufficient.
∴ The number of books are more than 58 × 13 i.e. 754.
But 729 < 754.
∴ Correct answer = 784.
FINAL ANSWER-
Option 'b' i.e. '784' is the correct answer to the given question.
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