Question

23. Number of students studying in colleges A
and B are in the ratio of 3 : 4 respectively. If
50 more students join college A and there is
no change in the number of students in
college B, the respective ratio becomes 5:6.
What is the number of students in college B?
(a) 450 (b) 500 (c) 400
(d) 600 (e) None of these​

Answer 1

Answer:

Step-by-step explanation:

Suppose total number of students in  

College A = 3x and total number of students in

College B = 4x.

After 50 more students join College A,  

new ratio = 3x + 50/4x = 5/6

= 18x + 300 = 20x= 2x = 300

∴ x = 150

∴ Total number of students in college B = 4 x 150 = 600

Answer 2

Answer:

There are 600 students studying in college B. Hence option (d) is correct.

Step-by-step explanation:

To find:-

The number of students in college B.

According to the question,

Let the common ratio be y.

The ratio of the number of students studying in college A and B is 3:4, i.e.,

The number of the students studying in college A = 3y

And the number of students studying in college B = 4y

Now,

50 more students join the college A, i.e.,

The number of students in college A = 3y + 50

Then,

The new ratio = 5:6

⇒ (3y + 50)/4y = 5/6

Cross multiply the equation as follows:

6(3y + 50) = 5(4y)

18y + 300 = 20y

18y - 20y = -300

         -2y = -300

            y = 150

So,

The number of students studying in college B is,

= 4y

= 4(150)

= 600 students

Therefore, there are 600 students studying in college B.

Option (d) is the correct answer.

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