No of students in a college?

There are two colleges in the town.- college A and college B.there are 500 students more in college A than in college B .The ratio of boys to that of the girls in college A is 3:2 and in college B is 4:1.The ratio of number of science ,humanities and commerce students in college A and college B are respectively 2:5:3 and 2:3:3. The number of commerce students in both the colleges is same. How many students are there in college A.?

No of students in a college?
B + 500 = A





Based on commerce students, 3B/8 = 3A/10





3B/8 = 3(B+500)/10





Cross multiplying,


30B = (8)(3B + 1500)


30B = 24B + 12000


6B =12000


B = 2000





So, there are 2000 students in college B, and B+500 = A = 2500 students in college A.
Reply:2500





With the given data, will have to figure that each college only has 3 programs ... Science, Humanities and Commerce.





They both have the same number of Commerce Students ... Set that to variable "C".





We know that for college A the ratio produces a total student population of





3C+5C+2C





For college B the total student populatio would be


3C+3C+2C





And we know that there are 500 more students in College A.





Therefore


College A = College B+500


3C+5C+2C=3C+3C+2C+500





10C=8C+500


2C=500





C=250. Remember C is the number of commerce students. Pug back into the ratios to get the numbers for each college.





Students At A=2500


Students at B=2000








2500
Reply:Let A = the number of students in college A ∴ A − 500 students = the number of students in college B,





Satisfies “There are 500 students more in college A than in college B.”





“The ratio of number of science, humanities and commerce students in college A and college B are respectively 2:5:3 and 2:3:3. The number of commerce students in both the colleges is same.”





2:5:3, the number of commerce is the same. Assuming that each student only took these three classes 3/(2+5+3) = 0.3 of the students took commerce in college A.





2:3:3, the number of commerce is the same. 3/(2+3+3) = 0.375 of the students took commerce in college A.





0.3A = 0.375(A − 500 students)


0.3A = 0.375A − 187.5 students


0.075A = 187.5 students


A = 2,500 students
Reply:Let students in college A be A and that in college B be B


Then A = B + 500


The statements regarding the ratio of oys and girls is not useful.


Let in college A


number of science be 2x


humanities be 5x


and commerce students be 3x


so in college A number of students = 10x


And


Let in college B


number of science be 2y


humanities be 3y


and commerce students be 3y


so in college A number of students = 8y


But commerce students in both are same


therefore, 3x = 3y


i.e. x = y


A = B + 500


so 10 x = 8y + 500


10 x = 8x + 500 -------as x = y


2 x = 500


x = 250


students in college A = 10x = 2500


and in B = 2500 – 500 = 2000


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