Aptitude Question: Download Questions PDF
Ten boxes are there. Each ball weighs 100 gms. One ball is weighing 90 gms.
i) If there are 3 balls (n=3) in each box, how many times will it take to find 90 gms ball?
ii) Same question with n=10
iii) Same question with n=9
Answer:
If n=3 then answer is:1
Take two balls and weigh. If both are equal then remaning ball is 90 gms
else if second is less than first one then second ball is 90gms
else if first is less than second on then first ball is 90 gms
If n=10 answer is: 3
Divide the n=10 into two 5-sub groups
compare the both the groups
If 1group<2group then 90 gms ball is present in the first group
else it is present in the second group.
Take the less weight group and divide it into 2-2-1 subgroup.
Now compare the 2-subgroups first. If first 2-subgroup is less than the second 2-subgroup then 90gms is present in the first 2-subgroup otherwise it is present in the second 2-subgroup. If both are equal then the remaing 1-subgroup ball is 90gms ball.
Now take less weigth subgroup of 2-subgroups. Now compare the two balls that are existing in the 2-subgroup group. Then we can find the 90 gms ball.
So we require 3 chances for detection of 90 gms ball when n=10
If n=9 then answer is :3
Take two balls and weigh. If both are equal then remaning ball is 90 gms
else if second is less than first one then second ball is 90gms
else if first is less than second on then first ball is 90 gms
If n=10 answer is: 3
Divide the n=10 into two 5-sub groups
compare the both the groups
If 1group<2group then 90 gms ball is present in the first group
else it is present in the second group.
Take the less weight group and divide it into 2-2-1 subgroup.
Now compare the 2-subgroups first. If first 2-subgroup is less than the second 2-subgroup then 90gms is present in the first 2-subgroup otherwise it is present in the second 2-subgroup. If both are equal then the remaing 1-subgroup ball is 90gms ball.
Now take less weigth subgroup of 2-subgroups. Now compare the two balls that are existing in the 2-subgroup group. Then we can find the 90 gms ball.
So we require 3 chances for detection of 90 gms ball when n=10
If n=9 then answer is :3
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