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Problem on ratios

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by Vishnu88 » Mon Apr 04, 2011 10:49 am
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3
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by GMATGuruNY » Mon Apr 04, 2011 12:55 pm
Vishnu88 wrote:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3
The following method is called alligation. It's an easy way to handle weighted average problems.

In the problem above, we want to combine an 11% decrease with a 7% increase to yield a total increase of 1%.
Thus, we need to know what ratio of (-11%) : (+7%) will yield a total increase of +1%.

The proportion needed of each starting percentage is the positive difference between the other 2 percentages.

Proportion needed of -11% = positive difference between the other 2 percentages = 7-1 = 6.
Proportion needed of 7% = positive difference between the other 2 percentages = 1-(-11) = 12.

Ratio of (-11%) : (+7%) = 6:12 = 1:2.

The correct answer is A.
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by Anurag@Gurome » Mon Apr 04, 2011 7:03 pm
Solution:
Let the revenue from car sales in 1996 be 'c'.
So, the revenue from car sales in 1997 was c * (1 - 11/100) = 89c/100.
Let the revenue from truck sales in 1996 be 't'.
So, the revenue from truck sales in 1997 was t*(1 + 7/100) = 107t/100.
Total revenue from car sales and truck sales in 1996 was (c + t).
So, the revenue from car and truck sales in 1997 was (c+t)*(1 + 1/100) = (c+t)*101/100.
So, 89c/100 + 107t/100 = 101(c+t)/100.
Or, 6t/100 = 12c/100.
Or c/t = 6/12 = ½.
The correct answer is (A).
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by manpsingh87 » Mon Apr 04, 2011 9:56 pm
Vishnu88 wrote:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3
car sales in 1996= x, truck sales in 1996=y
car sales in 1997=.89x, truck sales in 1997=1.07y

also .89x+1.07y=1.01(x+y);
.12x=.06y;
x/y=6/12=1/2;
hence A
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