In a restaurant, the cost of providing a particular type of food is partly constant...

JAMB 1985

In a restaurant, the cost of providing a particular type of food is partly constant and partially inversely proportional to the number of people. If cost per head for 100 people is 30k and the cost for 40 people is 60k, Find the cost for 50 people?

A. 15k
B. 20k
C. 50k
D. 40k
E. 45k

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Correct Answer: Option C

Explanation

C = a + k

\(\frac{1}{N}\) = c

= \(\frac{aN + k}{N}\)

CN = aN + K

30(100) = a(100) + k

3000 = 100a + k.......(i)

60(40) = a(40) + k

2400 = 40a + k.......(ii)

eqn (i) - eqn (ii)

600 = 60a

a = 10

subt. for a in eqn (i) 3000 = 100(10) + K

3000 - 1000 = k

k = 2000

CN = 10N + 2000. when N = 50,

50C = 10(50) + 2000

50C = 500 + 2000

C = \(\frac{2500}{50}\)

= 50k

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