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:
In this question it is given that while packing 85 books in each bag, 9 bags were not filled completely. Another condition is given as while packing 58 books in each bag, 13 bags were not enough to pack all the books. It is also provided that he was able to pack the books in M bags each having M books.
So, books packed and more bags are 85 books and 9 bags and books packed and fewer bags are 58 books and 13 bags.
Here the concept of a square root can be used. A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.
The correct answer is: 784
Now we have given books packed and more bags are 85 books and 9 bags and books packed and fewer bags are 58 books and 13 bags. We have also given that there are M number of bags and M number of books in each bag.
Since there is M number of books, we have:
Here in this question, we have given that while packing 85 books in each bag, 9 bags were not filled completely. Another condition is given as while packing 58 books in each bag, 13 bags were not enough to pack all the books. It is also provided that he was able to pack the books in M bags each having M books. So via the square root concept, we found out that there are 784 books in total.
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