Question

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

Answer:

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

2nd example

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.

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Answer 2

Answer:

Step-by-step explanation: