Average length of the 5 wood pieces = 124 cm.
Total length of these 5 wood pieces = 124*5 cm = 620 cm.
To maximize the length of the shortest wood piece, we have to minimize the lengths of other pieces provided their total length remain 620 cm.
Median length is 140 cm => If the woods are arranged in increasing order of length the middle one will have length of 140 cm. This also implies that minimum length possible for the longest three (including the middle one) wood pieces is 140 cm.
Total length of longest three wood pieces = 140*3 cm = 420 cm.
Total length of other two wood pieces = (620 - 420) cm = 200 cm.
Now, maximum length possible for the shortest wood = (200/2) cm = 100 cm
[Other possible choices of lengths for these two wood pieces were: 80cm and 120 cm, 90 cm and 110 cm etc. But (100cm, 100cm) results in the maximum length of the shortest wood piece. Also this results in two shortest wood pieces, not one.]
The correct answer is B.
Rahul Lakhani
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