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Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders, and Rs. 600 when there are 50 boarders. What will be the average expense per boarder when there are 100 boarders?
- a)Rs. 550
- b)Rs. 580
- c)Rs. 540
- d)Rs. 570
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Total expenses of a boarding house are partly fixed and partly varying...
Let x be the fixed cost and y be the variable cost.
17,500 = x + 25y ……..(i)
30,000 = x + 50y ……..(ii)
Solving the equations (i) and (ii), we get
x = 5,000, y = 500
Now, if the average expense of 100 boarders be `A`, then
100 × A = 5,000 + 500 × 100
∴ A = 550
17,500 = x + 25y ……..(i)
30,000 = x + 50y ……..(ii)
Solving the equations (i) and (ii), we get
x = 5,000, y = 500
Now, if the average expense of 100 boarders be `A`, then
100 × A = 5,000 + 500 × 100
∴ A = 550
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Community Answer
Total expenses of a boarding house are partly fixed and partly varying...
To solve this problem, we can use the concept of linear equations. Let's break down the given information and solve step by step.
Let's assume that the fixed expenses of the boarding house are denoted by 'a' and the expenses varying linearly with the number of boarders are denoted by 'b'.
1. Given that the average expense per boarder is Rs. 700 when there are 25 boarders.
- This implies that the total expenses when there are 25 boarders can be represented as:
Total expenses = a + 25b
- And the average expense per boarder is given as Rs. 700, so:
(a + 25b) / 25 = 700
2. Given that the average expense per boarder is Rs. 600 when there are 50 boarders.
- This implies that the total expenses when there are 50 boarders can be represented as:
Total expenses = a + 50b
- And the average expense per boarder is given as Rs. 600, so:
(a + 50b) / 50 = 600
Now, we have two equations:
1. (a + 25b) / 25 = 700
2. (a + 50b) / 50 = 600
We can solve these two equations simultaneously to find the values of 'a' and 'b'.
Solving equation 1 for 'a', we get:
a = 700 * 25 - 25b
a = 17500 - 25b
Substituting this value of 'a' in equation 2, we get:
(17500 - 25b + 50b) / 50 = 600
17500 + 25b = 600 * 50
17500 + 25b = 30000
25b = 30000 - 17500
25b = 12500
b = 12500 / 25
b = 500
Now, substituting the value of 'b' in equation 1, we get:
a = 17500 - 25 * 500
a = 5000
Therefore, the fixed expenses (a) are Rs. 5000 and the expenses varying linearly with the number of boarders (b) are Rs. 500.
Finally, to find the average expense per boarder when there are 100 boarders:
Total expenses = a + 100b
Total expenses = 5000 + 100 * 500
Total expenses = 5000 + 50000
Total expenses = 55000
Average expense per boarder = Total expenses / Number of boarders
Average expense per boarder = 55000 / 100
Average expense per boarder = Rs. 550
Hence, the correct answer is option 'A', Rs. 550.
Let's assume that the fixed expenses of the boarding house are denoted by 'a' and the expenses varying linearly with the number of boarders are denoted by 'b'.
1. Given that the average expense per boarder is Rs. 700 when there are 25 boarders.
- This implies that the total expenses when there are 25 boarders can be represented as:
Total expenses = a + 25b
- And the average expense per boarder is given as Rs. 700, so:
(a + 25b) / 25 = 700
2. Given that the average expense per boarder is Rs. 600 when there are 50 boarders.
- This implies that the total expenses when there are 50 boarders can be represented as:
Total expenses = a + 50b
- And the average expense per boarder is given as Rs. 600, so:
(a + 50b) / 50 = 600
Now, we have two equations:
1. (a + 25b) / 25 = 700
2. (a + 50b) / 50 = 600
We can solve these two equations simultaneously to find the values of 'a' and 'b'.
Solving equation 1 for 'a', we get:
a = 700 * 25 - 25b
a = 17500 - 25b
Substituting this value of 'a' in equation 2, we get:
(17500 - 25b + 50b) / 50 = 600
17500 + 25b = 600 * 50
17500 + 25b = 30000
25b = 30000 - 17500
25b = 12500
b = 12500 / 25
b = 500
Now, substituting the value of 'b' in equation 1, we get:
a = 17500 - 25 * 500
a = 5000
Therefore, the fixed expenses (a) are Rs. 5000 and the expenses varying linearly with the number of boarders (b) are Rs. 500.
Finally, to find the average expense per boarder when there are 100 boarders:
Total expenses = a + 100b
Total expenses = 5000 + 100 * 500
Total expenses = 5000 + 50000
Total expenses = 55000
Average expense per boarder = Total expenses / Number of boarders
Average expense per boarder = 55000 / 100
Average expense per boarder = Rs. 550
Hence, the correct answer is option 'A', Rs. 550.
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Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders, and Rs. 600 when there are 50 boarders. What will be the average expense per boarder when there are 100 boarders?a)Rs. 550b)Rs. 580c)Rs. 540d)Rs. 570Correct answer is option 'A'. Can you explain this answer?
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