Question 31898: Five men took turns weighing themselves on a scale. However, they weighed each other two at a time, ten times total , so that every possible combination of two men was weighed. The scale had the following readouts for the pairs: 236 pounds, 244 pounds, 228 pounds, 250 pounds, 258 pounds, 230 pounds, 246 pounds, 238 pounds, 242 pounds, and 252 pounds.
How heavy was the heaviest man?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Five men took turns weighing themselves on a scale. However, they weighed each other two at a time, ten times total , so that every possible combination of two men was weighed. The scale had the following readouts for the pairs: 236 pounds, 244 pounds, 228 pounds, 250 pounds, 258 pounds, 230 pounds, 246 pounds, 238 pounds, 242 pounds, and 252 pounds.
How heavy was the heaviest man?
LET THE WEIGHTS 5 MEN IN ORDER OF DECREASING WEIGHT BE A,B,C,D,E
WHEN THEY WEIGH IN PAIRS WE GET 5C2=5*4/2=10 DIFFERENT PAIRS OR 20 MEN
HENCE THE TOTAL WEIGHT IS FOUR TIMES THE WEIGHT OF THE 5 MEN'S TOTAL WEIGHT
4(A+B+C+D+E)=236+244+228+250+258+230+246+238+242+252=2424
A+B+C+D+E=606..............I
NOW HEAVIEST IS A+B=258.........II
NEXT HEAVY IS A+C=252...........III
LIGHTEST =D+E=228.................IV
EQN.I-EQN.IV...GIVES..
A+B+C+D+E-D-E=606-228=374
A+B+C=374.....................V
EQN.II+EQN.III GIVES
A+B+A+C=258+252=510
2A+B+C=510.................VI
EQN.VI-EQ.EQN.V...GIVES...
2A+B+C-A-B-C=510-374=136
A=136
SO HEAVIEST MAN'S WEIGHT =136
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