In a room, there are \(n\) persons whose average height is \(160 \ \text{cm}\). If \(m\) more persons, whose average height is \(172 \ \text{cm}\), enter the room, then the average height of all…
Question and options
In a room, there are persons whose average height is . If more persons, whose average height is , enter the room, then the average height of all persons in the room becomes . Then is
Answer and explanation
Correct answer: A - \(1 : 2\)
The total heights must balance: 160n + 172m = 164(n + m). This simplifies to 8m = 4n, so m : n = 1 : 2. The reversed ratio 2 : 1 mixes up which group is larger; the new average sits nearer 160, so the original group must be bigger.
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