gmat20092009 wrote:Guys i have a doubt

Suppose vlass A has boys girls in ratio 5:4
Class B has boys girls in ratio 7:8

When we mix boys and girls of class A and B in class C ratio of boys:girls becum 22:29

Doubt is how to frame the formula for class C.

The situation above is impossible. If 5/9 of the students in one class are boys, and 7/15 of the students in the other class are boys, when we combine the classes the fraction which are boys must be somewhere between 7/15 and 5/9. So it's impossible for the ratio of boys to girls in the combined classes to be 22:29; that would mean 22/51 of all students are boys, and that's less than 7/15.

Suppose instead the ratio of boys to girls in the combined class is 22:23; that's mathematically possible. From the information in the question, we can find the ratio of the two class sizes. You can use weighted average principles here (we have one group with an average of 7/15 = 21/45, another with an average of 5/9 = 25/45, and a combined average of 22/45. By finding the distances from each group's average to the combined average, we can find the ratio of the groups; so 1 to 3 is the ratio of the size of class A to the size of class B.

If you don't understand weighted averages in this way, you can do this algebraically. It may be easier to rewrite the ratios so each is out of 45:

Class A: 25 to 20
Class B: 21 to 24
Class A+B: 22 to 23

If we have A students in class A, and B students in class B, we can add the number of boys from each class, and equate that to the total number of boys in the combined classes:

(25/45)A + (21/45)B = (22/45)(A + B)
25A + 21B = 22A + 22B
3A = B
A/B = 1/3

There are other ways to set up the algebra here, of course.