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The total expense of a boarding house are partly fixed and partly variable with the number of boarders. The charge is Rs.70 per head when there are 25 boarders and Rs.60 when there are 50 boarders. Find the charge per head when there are 100 boarders.
- a)65
- b)55
- c)50
- d)45
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The total expense of a boarding house are partly fixed and partly vari...
Let a = fixed cost and k = variable cost and n = number of boarders
total cost when 25 boarders c = 25*70 = 1750 i.e. 1750 = a + 25k
total cost when 50 boarders c = 50*60 = 3000 i.e. 3000 = a + 50k
solving above 2 eqns, 3000-1750 = 25k i.e. 1250 = 25k i.e. k = 50
therefore, substituting this value of k in either of above 2 eqns we get
a = 500 (a = 3000-50*50 = 500 or a = 1750 - 25*50 = 500)
so total cost when 100 boarders = c = a + 100k = 500 + 100*50 = 5500
so cost per head = 5500/100 = 55
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The total expense of a boarding house are partly fixed and partly vari...
Given,
- Charge per head when there are 25 boarders = Rs.70
- Charge per head when there are 50 boarders = Rs.60
Let the fixed expenses be F and the variable expenses per head be V.
Then, we can write two equations based on the given information:
1. 25V + F = 25 x 70
2. 50V + F = 50 x 60
Solving the above equations, we get:
V = -10 (variable expenses decrease by Rs.10 for every additional boarder)
F = 950 (fixed expenses)
Now, we need to find the charge per head when there are 100 boarders.
Let C be the charge per head when there are 100 boarders.
Using the equation for variable expenses, we can write:
100V + F = 100C
Substituting the values of V and F, we get:
100(-10) + 950 = 100C
C = 55
Therefore, the charge per head when there are 100 boarders is Rs.55.
- Charge per head when there are 25 boarders = Rs.70
- Charge per head when there are 50 boarders = Rs.60
Let the fixed expenses be F and the variable expenses per head be V.
Then, we can write two equations based on the given information:
1. 25V + F = 25 x 70
2. 50V + F = 50 x 60
Solving the above equations, we get:
V = -10 (variable expenses decrease by Rs.10 for every additional boarder)
F = 950 (fixed expenses)
Now, we need to find the charge per head when there are 100 boarders.
Let C be the charge per head when there are 100 boarders.
Using the equation for variable expenses, we can write:
100V + F = 100C
Substituting the values of V and F, we get:
100(-10) + 950 = 100C
C = 55
Therefore, the charge per head when there are 100 boarders is Rs.55.
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