Q48
A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight, in kg, of the heaviest box?
Answer: B
Let a, b, c, d and e be the weights, in kg ,of the five boxes with the shipping clerk, where,
a < b < c < d < e.
110 = a + b < a + c < ….. < c + e < d + e = 121
i.e. a + c = 112 and c + e = 120
Each box is weighed 4 times.
∴ 4a + 4b + 4c + 4d + 4e = 110 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 120 + 121 = 1156
∴ a + b + c + d + e = 289
Now it is clear that a + b = 110 and d + e = 121
∴ 110 + c + 121 = 289
∴ c = 58
Substituting this value in c + e = 120
∴ e = 62
Hence, option (b).