Question

Here are two examinations rooms a and

b. If 10 students are sent from a to b, then the number of students in each room is the same. If 20 candidates are sent from b to a, then the number of students in a is double the number of students in

b. The number of students in room a is:

Answer 1

Let the number of students in rooms A and B be x and y respectively.

Then, x - 10 = y + 10      x - y = 20 .... (i)

and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

Solving (i) and (ii) we get: mod of x = 100 , mod of y = 80.

The required answer A = 100.

Answer 2

Let no. of students in hall a be x an hall b be y.

If 10 students are sent from a to b,

No. of students in hall a=x-10

No. of students in hall b=y+10

Given that x-10=y+10

So y=x-20.............(1)

If 20 students are sent from b to a,

No. of students in hall a=x+20

No. of students in hall b=y-20

So x+20=2(y-20)

Using eq. (1),

x+20=2(x-20-20)

x+20=2(x-40)

x+20=2x-80

x=100

So students in hall a are 100