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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32222)