SOLUTION: In a class, average height of all students is 'a' cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. find the nu

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Question 1085526: In a class, average height of all students is 'a' cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. find the number of students in the class. (here a>c and b>c).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of students equal N.
So,
T%2FN=a
T=aN
and
b=T%5B10%5D%2F10
T%5B10%5D=10b
and
c=T%5BN-10%5D%2F%28N-10%29
T%5BN-10%5D=%28N-10%29c
and,
T=T%5BN-10%5D%2BT%5B10%5D
Substituting,
aN=%28N-10%29c%2B10b
aN=cN-10c%2B10b
aN-cN=10%28b-c%29
%28a-c%29N=10%28b-c%29
highlight%28N=10%28%28b-c%29%2F%28a-c%29%29%29