Jazzmin wrote:

In 1940 a certain company only had variable expenses and fixed expenses, both of which increased during the year. The companyś Variable expenses increased 10 percent and Fixed expenses increased 20 percent. If the companyś total expenses increased 15 percent from their original amount during 1940, then the companyś variable expenses, after the increase occurred are what fraction of its total expenses for the year?

1. 1/3

2. 1/4

3. 1/2

4. 11/23

5. 12/23

Detailed Method :We have only two types of expenses i.e. Variable expenses and Fixed Expenses

Let us denote Variable expenses = V

Fixed expenses = FTotal Expense = (V + F)

Variable expenses increased 10 percent means: V becomes 1.10V --- (I)Fixed expenses increased 20 percent means: F becomes 1.20F -----(II)

We know,

Total expenses increased 15 percent from their original amount : (V +F) becomes 1.15(V +F) -----(III)Now, (I) +(II) = (III)

1.10V + 1.20F = 1.15V + 1.15F

1.20F - 1.15F = 1.15V - 1.10V

0.05F = 0.05V

Or \(\frac{F}{V}\) = \(\frac{1}{1}\)------> (Original Ratio of F and V before the increase occurred)

Question is asking for the ratio of Variable expense to Fixed expense after the increase took place,

So, We want the ratio of \(\frac{1.10V}{1.15V+1.15F}\)

As F = V, replace F by V

\(\frac{1.10V}{1.15V +1.15V}\)

\(\frac{1.10V}{2.30V}\)

Solving it we get, \(\frac{11}{23}\)

Hence (D)

Weighted Average Method :V/F = 20-15/15-10

\(\frac{V}{F}\) =\(\frac{1}{1}\)

V increases 10% = 1 + 1*0.1 = 1.10

V (new)F increases 20% = 1 + 1*0.2 = 1.20

F (New)We want to find out \(\frac{V new}{V (new) + F (new)}\)

\(\frac{1.1}{1.1+1.20}\)

\(\frac{11}{23}\)

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