Multiple choice

In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m : n is

  1. 1 : 3

  2. 2 : 1

  3. 1 : 2

  4. 3 : 1
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C Correct answer
Explanation

Using the weighted average formula: 160n + 172m = 164(n + m). This simplifies to 160n + 172m = 164n + 164m, which leads to 8m = 4n, or m/n = 4/8 = 1/2.

AI explanation

Using the method of alligation or balancing the overall average, the ratio of the number of persons is determined by the differences from the final average. The initial group of n persons has an average height of 160 cm, which is 4 cm below the new average of 164 cm, creating a total deficit of 4n. The m new persons have an average height of 172 cm, which is 8 cm above the new average, creating a total excess of 8m. Equating the total deficit to the total excess gives 4n = 8m, which simplifies to the ratio m : n = 1 : 2.

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