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In 1940 a certain company only had variable expenses and fixed expense

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In 1940 a certain company only had variable expenses and fixed expense  [#permalink]

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New post Updated on: 13 Dec 2018, 08:59
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D
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Difficulty:

  75% (hard)

Question Stats:

49% (02:18) correct 51% (02:41) wrong based on 64 sessions

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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

I want to know what difficulty level this question is.

Originally posted by Jazzmin on 12 Dec 2018, 21:29.
Last edited by Jazzmin on 13 Dec 2018, 08:59, edited 1 time in total.
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Re: In 1940 a certain company only had variable expenses and fixed expense  [#permalink]

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New post 12 Dec 2018, 23:25
1
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 = F

Total 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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Re: In 1940 a certain company only had variable expenses and fixed expense  [#permalink]

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New post 12 Dec 2018, 23:50
2
To think Smartly…
Lets assume Both variable expenses and fixed expense is same. Suppose X.

Increase in Fixed Expense : X------1.2X
Increase in Variable Expense :X---- 1.1 X

Total:2X
Increase in Total Expense : 2.3 X

Question: Variable Expense/total Expense = 1.1X / 2.3 X = 11/23
Answer :D
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Re: In 1940 a certain company only had variable expenses and fixed expense  [#permalink]

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New post 22 Dec 2018, 02:20
I think it is a middle difficulty, but its words may be somehow confusing.

It initially said that the price is increased during 1940,
then mentioned a 15% increase from their original amount during 1940.
It may infer that there are 2 increases: i.e there is 15% increase after the original prices during 1940, which are already increased as mentioned at the start of the question.

It needs time to grasp what it really meant.

Besides, the question can be answered without the 15% increase info. this may add more confusion.
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Re: In 1940 a certain company only had variable expenses and fixed expense   [#permalink] 22 Dec 2018, 02:20
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