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Ratio question

by vinhaha » Tue Mar 08, 2016 4:44 am
Hi, can anybody help me with below question? I can solve it using a table, but not algebraically in a fraction as in my solution.

Question:
A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?

Solution
[spoiler](+5%)(100)+(-13%)(50) / (100 + 50) = (+5 - 6,5) / 150 = -1,5 / 150 = -1%
[/spoiler]
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by MartyMurray » Tue Mar 08, 2016 7:05 am
Pen Sales 2006 - P
Pencil Sales 2006 - L

1.05P + .87L = .99(P + L)

1.05P + .87L = .99P + .99L

.06P = .12L

P/L = [spoiler]2/1[/spoiler]

Alternate Method

Use allegation.

P 2007 up .05 from P 2006

L 2007 down .13 from L 2006

Spread .05 - (-.13) = .18

Change in total revenue -.01

-.01 is -.06 from .05 and .12 from -.13

So .01 is 2/3 of the .18 spread toward .05.

-.13________(2/3)________-.01___(1/3)___.05

So the 2006 revenue is 2/3 pens and 1/3 pencils.

P/L = (2/3)/(1/3) = [spoiler]2/1[/spoiler]
Last edited by MartyMurray on Tue Mar 08, 2016 5:42 pm, edited 1 time in total.
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by [email protected] » Tue Mar 08, 2016 10:39 am
Hi vinhaha,

There was a lengthy discussion of this question here:

https://www.beatthegmat.com/mgmat-percen ... 72217.html

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by Matt@VeritasPrep » Thu Mar 17, 2016 9:20 pm
You have to be careful when picking your own numbers here, since you don't know the number of pens and pencils in 2006. With that in mind, we could use variables:

Pencil revenue in 2006 = x
Pen revenue in 2006 = y

Pencil revenue in 2007 = .87x
Pen revenue in 2007 = 1.05y

We're also told that total revenue is down 1%, so

Revenue in '07 = 99% of Revenue in '06

.87x + 1.05y = .99*(x + y)

or

.87x + 1.05y = .99x + .99y

.06y = .12x

6y = 12x

y = 2x
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