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Combine Ratio Problem

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Combine Ratio Problem

by iwillsurvive101 » Thu May 24, 2012 4:40 pm
(This is from MGMAT CAT)

The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
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by iwillsurvive101 » Thu May 24, 2012 4:41 pm
How do you combine two ratios? Can someone please explain with few examples?
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by Anurag@Gurome » Thu May 24, 2012 8:41 pm
iwillsurvive101 wrote:(This is from MGMAT CAT)

The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
Given: In Class A, B : G = 3 : 4
In Class B, B : G = 4 : 5
In combined class, B : G = 17 : 22

Let the # of boys in class A = b and # of girls = g
Then in class B, # of boys = b - 1 and # of girls = g - 2
b : g = 3 : 4 implies 4b = 3g implies b = 3g/4
(b - 1) : (g - 2) = 4 : 5
5b - 5 = 4g - 8
5(3g/4) - 5 = 4g - 8
15g - 20 = 16g - 32
g = 12

Please note that the ratio of boys and girls for combined class is irrelevant in this question.
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by GMATGuruNY » Fri May 25, 2012 2:33 am
For a solution that avoids having to combine the ratios, check my post here:

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by ronnie1985 » Fri May 25, 2012 10:52 am
Class A : B = 3x G = 4x
Class B: B = 4y G = 5y

New ratio = (3x+4y)/(4x+5y) = 17/22

3x = 4y+1
4x = 5y+2

Solve for x and y

Class B girs = 10
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