Six persons, Akbar, Barry, Chand, Dhruv, Himesh and Gaurav, form a human pyramid, which has three levels. The first level consists of three persons who are standing on the ground, the second level consists of two persons who are standing on the shoulders of the three persons at the first level; the third level consists of one person who is standing on the shoulders of the two persons at the second level. Further, at each level, every person supports an equal weight and all the persons at a particular level together support the total weight of all the people on all the levels above them. The weights of the six persons are 50 kg, 60 kg, 70 kg, 80 kg, 90 kg and 100 kg, not necessarily in the same order. The following information is known about the persons at each level of the pyramid: i Akbar supports the same weight as Barry, which is not the same as the weight supported by Chand. ii. No one is standing on Himesh, but he does not weigh the least. ui. Dhruv, who weighs the most, is not at the same level as Chand, while Barry weighs more than each of Himesh and Gaurav iv. Chand weighs less than Gaurav and the weight of Gaurav is the average of the weights of Akbar and Barry. v Every person at the first level supports a weight of 70 kg .
who among following is standing at
the second level
Answers
Given : Six persons, Akbar, Barry, Chand, Dhruv, Himesh and Gaurav, form a human pyramid, which has three levels. The first level consists of three persons who are standing on the ground, the second level consists of two persons who are standing on the shoulders of the three persons at the first level; the third level consists of one person who is standing on the shoulders of the two persons at the second level. Further, at each level, every person supports an equal weight and all the persons at a particular level together support the total weight of all the people on all the levels above them.
To Find : who is is standing at the second level
Solution:
No one is standing on Himesh Hence Himesh is on Top
Akbar supports the same weight as Barry, Hence Akbar and Berry are at 1st or 2nd Level
Dhruv, who weighs the most, is not at the same level as Chand,
Hence one of them is at level 2
Hence Akbar and berry are at Level 1
H
G D/C
A B C/D
Every person at the first level supports a weight of 70 kg
Hence weight above them is 3 * 70 = 210 kg
Total weight = 450 kg Hence weight at Level 1 = 240 kg
Dhruv, weight the most = 100 kg
Barry weighs more than each of Himesh and Gaurav
Chand weighs less than Gaurav
=> Barry weighs more than each of Himesh and Gaurav and Chand
weight of Gaurav is the average of the weights of Akbar and Barry
Barry weighs more than Gaurav Hence Akbar weight less than Gaurav
=> Barry weighs more than each of Himesh and Gaurav , Akbar and Chand
Hence Barry weighs = 90 kg Dhruv, weight = 100 kg
weight of Gaurav is the average of the weights of Akbar and Barry
Akbar weight = 50 , 70 and Gaurav weight 70 , 80
if Akbar weigh 70 then Akbar + Berry = 160 kg Hence Gaurav = 80 kg
but then C/D = 240 - 160 = 80 kg Hence contradicts
so Akbar = 50 Barry = 90 , Gaurav = 70
Dhruv = 100
50 + 90 + 100 = 240 hence Dhruv is at 1st level
H
G C
A B D
Hence Gaurav and Chand are at level 2
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