In a restaurant, the cost of providing a particular type of food is partly constant and partly inversely proportional to the number of people. If the cost per head for 100 people is \(30 \mathrm{k}\) and the cost for 40 people is \(60 \mathrm{k}\), find the cost for 50 people.

A. \(15 \mathrm{k}\)
B. \(45 \mathrm{k}\)
C. \(20 \mathrm{k}\)
D. \(50 \mathrm{k}\)  
E. \(40 k\)

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Correct Answer: D