Some questions are quite creative. They are original and force you to think.
“Four children decided to find out their total mass. As they did not want their friends to know their individuals mass, the children decided to weigh themselves 3 persons at a time. Although the children tried all possible ways of grouping themselves into threes for weighing, only four different readings were repeatedly recorded on the weighing scale.
99.5 kg
108.1 kg
111.7 kg
116.3 kg
Find the combined mass of the heaviest child and the lightest child.”
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Solution:
Rank the kids according to their weight. Label them A, B, C, D. We know A is the lightest, followed by B and C, and D is the heaviest.
So, A+B+C = 99.5 ——(1)
and B+C+D = 116.3 —–(2)
the other combinations are A+B+D and A+C+D. Since C is > B, A+C+D = 111.7 —–(3)
and A+B+D = 108.1 —–(4)
(1)+(2) = A + 2B + 2C + D = 99.5+116.3=215.8
(3)+(4) = 2A + B + C + 2D = 111.7+108.1 = 219.8
multiply by 2:
2* ((3)+(4)) = 4A + 2B + 2C + 4D = 439.6
subtract (1)+(4) = 3A + 3D = 439.6 – 215.8 = 222.8
so A + D = 222.8/3 = 74.6kg
add all the masses –> this will give 3 sets of total mass –> 99.5 kg +108.1 kg + 111.7 kg+
116.3 kg = 435.6 = 3 *(A+B+C+D)
so, (A+B+C+D)= 435.6 / 3 = 145.2
with this total mass, the heaviest and lightest can be determined easily
heaviest –> 145.2 kg – 99.5kg= 45.7 kg
lightest –> 145.2 kg – 116.3 kg = 28.9 kg
heaviest +lightest –> 45.7 kg + 28.9 kg = 74.6 kg