Question

There are some students in the two examination halls A and B.to make the number of students equal in each hall 10 students are sent from A to B .but if 20 students are sent fromB to A the number of students in A becomes double the number of students in B. find the number of students in the two halls

Answer 1

Let a and b be the number of students in halls A and B respectively, such that a > b.

Then, if 10 students are transferred from a to b, the number of students are equal.

Therefore, a-10 = b+10

or a - b = 20 ---------- (1)

Similarly, if 20 students are sent from hall B to hall A, then the number of students in Hall A would be twice that of the students in Hall B.

Then, a+20 = 2(b-20)

or a + 20 = 2b - 40

or 2b - a = 60 ------- (2)

Adding equations (1) and (2), we get

2b - a = 60
a - b = 20

Therefore, on adding we get, b = 80

Substituting the value of b = 80 in equation 1, we get

a - 80 = 20

or a = 100.

Therefore there are 100 students in Hall A and 80 students in Hall B.

Answer 2

Answer:

Hall A =100 ,Hall B = 80

Step-by-step explanation:

Let the number of students in halls A and B are x and y, respectively.

Now, by given condition,                x-10=y+10

⇒ x – y = 20   ---> x-y-20  =0                                 … (i)

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

⇒ x-2y = -60                                                              …(ii)

On subtracting Eq. (i) from Eq. (ii), we get

(x-y-20)-(x- 2 y) = 60

x-y-20

-x+2y=60

x-y-x+2y=60+20

y=80....

On putting y = 80 in Eq. (i), we get

x – 80 = 20 => x = 100 and     y = 80

Hence, 100 students are in hall A and 80 students are in hall B.