Question

Three sets of english, mathematics and science books containin 336, 240 and 96 books respectively have to be sacked in such a wy that all the books are stored subjict-wise and the height of each stack os the same. total number of stacks will be

Answer 1

Firstly to arrange the books according to condition,
Find HCF of 336, 240 and 96.
Factors of 336,
2_|_336
2_|_168
2_|_84
2_|_42
3_|_21
7_|_7
_|_1
336 = 2×2×2×2×3×7
Factors of 240,
2_|_240
2_|_120
2_|_60
2_|_30
3_|_15
5_|_5
_|_1
240 = 2×2×2×2×3×5
Factors of 96,
2_|_96
2_|_48
2_|_24
2_|_12
2_|_6
3_|_3
_|_1
96 = 2×2×2×2×2×3

HCF (336,240,96) = 2×2×2×2×3
= 48
There are only 48 books in each stack.

Now,
Number of stacks of English books
= 336/48
= 7
Number of stacks of Mathematics books
= 240/48
= 5
Number of stacks of Science books
= 96/48
= 2
Hence, total number of stacks
= 7 + 5 + 2
= 14
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