Question 1:
Ajay 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 Ajay have?
Answers
The complete question is -
Ajay 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 Ajay have?
a. 765
b. 812
c. 729
d. 784
Given:
Books packed and more bags = 85 books and 9 bags
Books packed and less bags = 58 books and 13 bags
Books packed in = M bags
To Find:
How many books did Ajay have
Solution:
Total books = M x M = M²
Now, only option c and d which are 729 and 784 are perfect squares.
Thus,
58 books and 13 bags
= 58 x 13 = 754
754> 729.
Thus, 784 bags will be sufficient.
Answer: Ajay had 784 books.