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There were 35 students in a hostel. If the number of students increases by 7. the expenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)
Correct answer is '420'. Can you explain this answer?
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Verified Answer
There were 35 students in a hostel. If the number of students increase...
Suppose the average expenditure was ? x.
Then total expenditure = 35x. When 7 more students join the mess, total expenditure = 35*+42.
Now. the average expenditure =
Now, we have
or, 35x+ 42 = 42x - 42
or, 7x = 84
Therefore, x = l 2
Thus the original expenditure of the mess = 35x12 = Rs. 420.
Then total expenditure = 35x. When 7 more students join the mess, total expenditure = 35*+42.
Now. the average expenditure =
Now, we have
or, 35x+ 42 = 42x - 42
or, 7x = 84
Therefore, x = l 2
Thus the original expenditure of the mess = 35x12 = Rs. 420.
Most Upvoted Answer
There were 35 students in a hostel. If the number of students increase...
Given Information:
- Initially, there were 35 students in a hostel.
- After the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day.
- The average expenditure per head diminishes by Rs. 1.
Objective:
To find the original expenditure of the mess.
Solution:
Let's assume the original expenditure of the mess is 'x' Rs.
Step 1: Calculate the new average expenditure per head.
The original average expenditure per head can be calculated by dividing the original expenditure of the mess by the number of students:
Original average expenditure per head = x / 35 Rs.
After the number of students increases by 7, the average expenditure per head diminishes by Rs. 1. So, the new average expenditure per head can be calculated as follows:
New average expenditure per head = (x + 42) / 42 Rs.
According to the given information, the new average expenditure per head is Rs. 1 less than the original average expenditure per head:
(x + 42) / 42 = x / 35 - 1
Step 2: Solve the equation.
To solve the equation, we can cross-multiply:
35(x + 42) = 42(x / 35 - 1)
Simplifying the equation:
35x + 35(42) = 42x - 42(35)
35x + 1470 = 42x - 1470
Moving the variables to one side and the constants to the other side:
42x - 35x = 1470 + 1470
7x = 2940
Dividing both sides of the equation by 7:
x = 420
Conclusion:
The original expenditure of the mess is Rs. 420.
- Initially, there were 35 students in a hostel.
- After the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day.
- The average expenditure per head diminishes by Rs. 1.
Objective:
To find the original expenditure of the mess.
Solution:
Let's assume the original expenditure of the mess is 'x' Rs.
Step 1: Calculate the new average expenditure per head.
The original average expenditure per head can be calculated by dividing the original expenditure of the mess by the number of students:
Original average expenditure per head = x / 35 Rs.
After the number of students increases by 7, the average expenditure per head diminishes by Rs. 1. So, the new average expenditure per head can be calculated as follows:
New average expenditure per head = (x + 42) / 42 Rs.
According to the given information, the new average expenditure per head is Rs. 1 less than the original average expenditure per head:
(x + 42) / 42 = x / 35 - 1
Step 2: Solve the equation.
To solve the equation, we can cross-multiply:
35(x + 42) = 42(x / 35 - 1)
Simplifying the equation:
35x + 35(42) = 42x - 42(35)
35x + 1470 = 42x - 1470
Moving the variables to one side and the constants to the other side:
42x - 35x = 1470 + 1470
7x = 2940
Dividing both sides of the equation by 7:
x = 420
Conclusion:
The original expenditure of the mess is Rs. 420.
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There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer?
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There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer?.
There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There were 35 students in a hostel. If the number of students increases by 7. theexpenses of the mess increase by Rs. 42 per day while die average expenditure per head diminishes by Rs. 1. The original expenditure of the mess is___________Rs . (The answer should be an integer)Correct answer is '420'. Can you explain this answer?.
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