Answer Posted / guest

They weigh 54, 56, 58, 59, 62 pounds.

Let's assume that the weight of five bales are B1, B2, B3,
B4 and B5 pounds respectively. Also, B1 <= B2 <= B3 <= B4 <= B5

It is given that five bales of hay are weighed two at a time
in all possible ways. It means that each of the bale is
weighted four times.

Thus,

4*(B1 + B2 + B3 + B4 + B5) = (110 + 112 + 113 + 114 + 115 +
116 + 117 + 118 + 120 + 121)

4*(B1 + B2 + B3 + B4 + B5) = 1156

(B1 + B2 + B3 + B4 + B5) = 289 pounds

Now, B1 and B2 must add to 110 as they are the lightest one.

B1 + B2 = 110

Similarly, B4 and B5 must add to 121 as they are the
heaviest one.

B4 + B5 = 121

From above three equation, we get B3 = 58 pounds

Also, it is obvious that B1 and B3 will add to 112 - the
next possible higher value. Similarly, B3 and B5 will add to
120 - the next possible lower value.

B1 + B3 = 112

B3 + B5 = 120

Substituting B3 = 58, we get B1 = 54 and B5 = 62

From 2 & 3 equations, we get B2 = 56 and B4 = 59

Hence, the weight of five bales are 54, 56, 58, 59 and 62
pounds.

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