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# A toy company sells only toy cars and toy bikes. The revenue from toy

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Math Expert
Joined: 02 Sep 2009
Posts: 58410
A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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24 Sep 2018, 05:51
00:00

Difficulty:

35% (medium)

Question Stats:

85% (02:34) correct 15% (02:46) wrong based on 39 sessions

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A toy company sells only toy cars and toy bikes. The revenue from toy car sales in 2002 was down 11 percent from 2001 and the revenue from toy bikes sales in 2002 were up 7 percent from 2001. If total revenues from toy car sales and toy bikes sales in 2002 were up 1 percent from 2001, what is the ratio of revenue from toy car sales in 2001 to revenue from toy bikes sales in 2001?

(A) 1:2
(B) 2:3
(C) 4:5
(D) 3:2
(E) 7:5

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Re: A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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24 Sep 2018, 07:23
1
Bunuel wrote:
A toy company sells only toy cars and toy bikes. The revenue from toy car sales in 2002 was down 11 percent from 2001 and the revenue from toy bikes sales in 2002 were up 7 percent from 2001. If total revenues from toy car sales and toy bikes sales in 2002 were up 1 percent from 2001, what is the ratio of revenue from toy car sales in 2001 to revenue from toy bikes sales in 2001?

(A) 1:2
(B) 2:3
(C) 4:5
(D) 3:2
(E) 7:5

in 2001
Car revenue = c
Bikes revenue = b
Total revenue = b+c

in 2002
Car revenue = 0.89c
Bikes revenue = 1.07b
Total revenue = 1.01(b+c)
But new Revenue, 1.01(b+c) = 0.89c+1.07b

i.e. c/b = 1/2

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A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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24 Sep 2018, 08:38
2001: C+B=R
2002: .89C+1.07B=1.01R

Multiple the 2001 equation by 0.89 and then substract it from the second equation to get rid of C.
.18B=.12R
B=2/3R
C=1/3R

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Re: A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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24 Sep 2018, 10:20
The 1 percent up from 2001 is a weighted average between the car and bike sales. Being x the weight of the car sales:

$$0,01 = -0,11x + 0,07(1-x)$$
$$0,01 = -0,11x + 0,07 - 0,07x$$
$$0,06 = 0,18x$$
$$x = 1/3$$

Thus, the weight of the bike sales is $$2/3$$ and the ratio of revenue from car to bikes is $$1:2$$

Correct option: A
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Re: A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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24 Sep 2018, 12:00
If we consider total revenue from toy bike sales and toy car sales in 2001 to be 'b' and 'c' respectively.

0.01(b+c)=-0.11c + 0.07b
0.12c=0.06b
c/b=1/2

So ratio of toy car sales to bike sale in 2001 is 1:2.
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Re: A toy company sells only toy cars and toy bikes. The revenue from toy  [#permalink]

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27 Sep 2018, 17:22
1
Bunuel wrote:
A toy company sells only toy cars and toy bikes. The revenue from toy car sales in 2002 was down 11 percent from 2001 and the revenue from toy bikes sales in 2002 were up 7 percent from 2001. If total revenues from toy car sales and toy bikes sales in 2002 were up 1 percent from 2001, what is the ratio of revenue from toy car sales in 2001 to revenue from toy bikes sales in 2001?

(A) 1:2
(B) 2:3
(C) 4:5
(D) 3:2
(E) 7:5

Let C denote the revenue from toy car sales in 2001 and B denote the revenue from toy bike sales in 2001.

We can create the equation:

0.89C + 1.07B = 1.01(C + B)

0.89C + 1.07B = 1.01C + 1.01B

0.06B = 0.12C

0.06/0.12 = C/B

1/2 = C/B

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Re: A toy company sells only toy cars and toy bikes. The revenue from toy   [#permalink] 27 Sep 2018, 17:22
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