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There are some students in group A and group B. If one student goes from group A to group B, then the number of students in both groups is same. But one student goes from group B to group A, then the number of students in group A becomes twice of gro…

Q.5 (ii) There are some students in group A and group B. If one student goes from group A to group B, then the number of students in both groups is same. But one student goes from group B to group A, then the number of students in group A becomes twice of group B. Find the number of students in each group.

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Answer: Group A has 7 students and group B has 5 students.

Let group A have \(x\) students and group B have \(y\) students.

If one student goes from A to B, the numbers become equal:
\(x - 1 = y + 1 \Rightarrow x - y = 2\) … (1)

If one student goes from B to A, A becomes twice B:
\(x + 1 = 2(y - 1) \Rightarrow x - 2y = -3\) … (2)

Subtracting (2) from (1): \(y = 5\). Then from (1), \(x = 5 + 2 = 7\).

Check: \(7 - 1 = 6 = 5 + 1\) ✓ and \(7 + 1 = 8 = 2(5 - 1)\) ✓.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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