Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.

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A = 100 and B = 80

A = 110 and B = 90

A = 120 and B = 70

A = 130 and B = 60

answer is A.

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Detailed Solution

Given, students are divided into two groups A & B,

10

students are sent from A to B, the number in each is the same. But if

20

students are sent from B to A, the number in A is double the number in B.
Let the number of students in A and B be a and b respectively.
As per the question,

a - 10 = b + 10

\Rightarrow a - b = 20 . . . (1)

Therefore,

a + 20 = 2 (b - 20)

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

Subtracting (2) from (1), we get

a - b - (a - 2 b) = 20 - (- 60)

⟹ b = 80

Putting

b = 80

in (1), we get

a = 80 + 20 = 100

Therefore, number of students in group A is 100 and B is 80.
Hence, correct option is 1.

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