Question

A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kgs. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kgs. What is the weight, in kgs, of the heaviest box?

• A. 60 kg
• B. 62 kg
• C. 64 kg
• D. Can't be determined

Hint:

In sum-of-pairs problems, assign variables in ascending order and use smallest/largest sums to deduce step-by-step.

Answer 1

The Correct Option is B

Let the boxes weigh $a<b<c<d<e$. Step 1: Smallest and largest sums Smallest sum $a+b = 110$, largest sum $d+e = 121$. Step 2: Use next smallest sum Next smallest is $a+c = 112 \Rightarrow c = 112 - a$. Step 3: Use next largest sum Next largest is $c+e = 120 \Rightarrow e = 120 - c$. Step 4: Relation from $c$ and $e$ Substitute $c = 112-a$ into $e$: $e = 120 - (112 - a) = a + 8$. Step 5: Use $d+e = 121$ $d + (a+8) = 121 \Rightarrow d = 113 - a$. Step 6: Use $b+e$ from list $b+e$ should appear in sums; since $b$ is just above $a$, and $b+c$ is in the list, after testing possible $a$, only $a = 54$ satisfies all sums. Then: $a=54,\ b=56,\ c=58,\ d=59,\ e=62$. Heaviest = $e = 62$ kg. \[ \boxed{62\ \text{kg}} \]