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5. The total expenditure (E) of a mess is given by E = F cn , where F is the fixed cost, n is the number of people eating in the mess and c is the cost per person. In one month, F, n and c increased by 50%, 25% and 20% respectively over the previous month. What is the percentage increase in the total expenditure?
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5. The total expenditure (E) of a mess is given by E = F cn , where ...
Solution:

Understanding the problem:
We are given the formula for calculating the total expenditure of a mess. In one month, the fixed cost, number of people eating in the mess and the cost per person have increased by 50%, 25% and 20% respectively over the previous month. We need to find the percentage increase in the total expenditure.

Calculating the new values:
Let the original values of F, n and c be F0, n0 and c0 respectively.
Given that the new values are 150% of the old values for F, 125% of the old values for n and 120% of the old values for c.
This can be expressed as:
F = 1.5F0
n = 1.25n0
c = 1.2c0

Calculating the new total expenditure:
Substituting the new values in the given formula, we get:
E = Fcn
E = (1.5F0)(1.25n0)(1.2c0)
E = 2.25F0n0c0

Calculating the percentage increase:
Let the old total expenditure be E0.
Then, the percentage increase in the total expenditure can be calculated as:
% increase = ((E - E0) / E0) x 100
% increase = ((2.25F0n0c0 - E0) / E0) x 100

Simplifying the expression:
E0 = F0n0c0
% increase = ((2.25F0n0c0 - F0n0c0) / F0n0c0) x 100
% increase = (1.25 x 1.2 x 1.5 - 1) x 100
% increase = 87.5%

Conclusion:
Hence, the percentage increase in the total expenditure is 87.5%.
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5. The total expenditure (E) of a mess is given by E = F cn , where F is the fixed cost, n is the number of people eating in the mess and c is the cost per person. In one month, F, n and c increased by 50%, 25% and 20% respectively over the previous month. What is the percentage increase in the total expenditure?
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5. The total expenditure (E) of a mess is given by E = F cn , where F is the fixed cost, n is the number of people eating in the mess and c is the cost per person. In one month, F, n and c increased by 50%, 25% and 20% respectively over the previous month. What is the percentage increase in the total expenditure? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 5. The total expenditure (E) of a mess is given by E = F cn , where F is the fixed cost, n is the number of people eating in the mess and c is the cost per person. In one month, F, n and c increased by 50%, 25% and 20% respectively over the previous month. What is the percentage increase in the total expenditure? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5. The total expenditure (E) of a mess is given by E = F cn , where F is the fixed cost, n is the number of people eating in the mess and c is the cost per person. In one month, F, n and c increased by 50%, 25% and 20% respectively over the previous month. What is the percentage increase in the total expenditure?.
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