A book seller has 175 English books 245 science books and 385 mathematics books. He wants to sell the books in a box, subject Wise in equal numbers. What will be the greatest number of the box required? Also find the number of books for each subject in a box?
Answers
Finding the HCF of 175, 245 and 385.
175 = 5 × 5 × 7
245 = 5 × 7 × 7;
385 = 5 × 7 × 11
The HCF of 175, 245 and 385 is the product of the two common factors 5 and 7,
Therefore, 5 × 7 = 35
Since each box contains equal number of books, thus the greatest possible number of boxes will be = 35
The number of English books in each box will be = 175/35=5
The number of Science books in each box will be = 245/35=7
The number of Maths books in each box will be = 385/35=11
Hence, the total number of books in each box will be -
= 5 + 7 + 11
= 23
The HCF of 175, 245 and 385 is the product of the common factors 5 and 7 i.e, 5x7=35 Since each box contains equal number of books, the greatest possible number of boxes-35 The number of English books in each box = 175+35-5 The number of Science books in each box = 245+35=7
The number of Maths books in each box= 385+3511
Hence, the total number of books in each box is 5+7+11=23.
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