Tricky!
Consider an area in the form of a square ABCD , in which the population resides. Assume that population is large and is uniformly distributed in this area. If there exists three hospitals at points 'A', 'B' and 'C' , and people consult the nearest hospital as and when needed, what would be the ratio of population load in Hospital A : Hospital B : Hospital C ?
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1 solution
Hospital-less townspeople D will split up into halves, choosing either to go to hospital A or hospital C considering hospital B is situated at the opposite corner. So we have
town A : town B : town C : town D
= 100% A : 100% B : 100% C : 50% A + 50% C.
Thus, now going by hospitals,
HA : HB : HC
= 1 TA + 0.5 TD : 1 TB : 1 TC + 0.5 TD.
= 1.5 : 1 : 1.5.
= 3 : 2 : 3