The expenses of a hostel are partly fixed and partly variable with the number of boarders. When there are 50 boarders the charge is Rs. 48 per head and when there are 30 boarders the charge is Rs. 60 per head. Find the charges when there are 120 boarders?

a)
40

b)
32

c)
42

d)
37.5

Correct answer is option 'D'. Can you explain this answer?

Question

The expenses of a hostel are partly fixed and partly variable with the number of boarders. When there are 50 boarders the charge is Rs. 48 per head and when there are 30 boarders the charge is Rs. 60 per head. Find the charges when there are 120 boarders?

a)
40
b)
32
c)
42
d)
37.5

Correct answer is option 'D'. Can you explain this answer?

Answer

Answer

Fixed amt = x; variable amt = y;
x+50y = 50×48=2400
x+30y = 30x60=1800
solving the above eqn , we get y = 30.
by applying y=30 in above eqns we get x = 900
so for 120 boarders total expense is
900+120×30 = 4500
hence 4500/1200 = 37.5 per boarder

Answer

► Let, F = Fixed Cost, K = variable cost, B= No of boarders, E= Total Expenditure
► Then, E= F + KB
⇒ 2400 = F + K50
⇒ 1800 = F + K30
⇒ K= 30, F = 900
► When there are 120 boarders the charge will be
⇒ E = 900 + 30(120)
⇒ E= 4500
Charge per boarder = 4500/120 = 37.5

Answer

Given:
- When there are 50 boarders, the charge is Rs. 48 per head.
- When there are 30 boarders, the charge is Rs. 60 per head.

To Find:
The charges when there are 120 boarders.

Approach:
We can assume that the expenses of the hostel are composed of both fixed and variable components. Let's call the fixed component F and the variable component V.

We are given two scenarios:
1. When there are 50 boarders, the charge is Rs. 48 per head.
2. When there are 30 boarders, the charge is Rs. 60 per head.

We can set up two equations based on these scenarios:

Equation 1: F + 50V = 50 * 48
Equation 2: F + 30V = 30 * 60

We can solve these equations simultaneously to find the values of F and V.

Solution:
Solving Equation 1 and Equation 2 simultaneously:

Subtracting Equation 2 from Equation 1:
(F + 50V) - (F + 30V) = (50 * 48) - (30 * 60)
20V = 240
V = 240 / 20
V = 12

Substituting the value of V in Equation 1:
F + 50 * 12 = 50 * 48
F + 600 = 2400
F = 2400 - 600
F = 1800

Now we have the values of F and V:
F = 1800 and V = 12

To find the charges when there are 120 boarders, we can use the formula:
Charges = F + 120 * V

Substituting the values of F and V:
Charges = 1800 + 120 * 12
Charges = 1800 + 1440
Charges = 3240

Therefore, the charges when there are 120 boarders is Rs. 3240.

Answer: Option D) 37.5

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