Solution Required
*
by*
KIRAN KISHORE
on
28-Aug-2016 20:26

a scale can only weigh items that are more than 70 kg, so 5 boys had to be weighed in pairs.

the 10 weights recorded were: 86,92,96,100,104,109,110,113,119,127.

what is the weight of the second heaviest boy?

(explain your logic)

SHANMUGA PRIYAN M
on
30-Aug-2016 18:51

67.5

VAIDYANATHAN T
on
9-Sep-2016 22:16

59

VAIDYANATHAN T
on
9-Sep-2016 22:25

Sum of weights of all boys = (86+92+96+....+127)/4 = 264.
Let A be weight of lightest boy, B be weight of 2nd lightest boy and so on (upto E)
A+B=86; D+E=127
Weight of 3rd heaviest/lightest boy = C = 264 - (127+86) = 51.
Second smallest weight combination is 92. This must be sum of weights of lightest and 3rd lightest boys.
(i.e) A+C=92
Since C=51, A =92.
Since A+B=86, B=45
Third smallest weight combination may be B + C or A + D
Clearly B=45 and C=51, therefore B + C =96
Thus B + C is the 3rd smallest weight combination.
Fourth smallest weight combination must be A+D
A+D=100
Since A=41, it follows D=59.
Since D+E=127, it follows E=68.
The values can be verified using the given weight combinations.
Answer: Weight of second heaviest boy is 59.