Multiple choice

In a group of students, the mean weight of boys is $65$ kg. and mean weight of girls is $55$ kg. If the mean weight of all students of group is $61$ kg, then the ratio of the number of boys and girls in the group is

  1. 2 : 3

  2. 3 : 1

  3. 3 : 2

  4. 4 : 3
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C Correct answer
Explanation

Using the weighted average formula: (65B + 55G) / (B + G) = 61. This simplifies to 65B + 55G = 61B + 61G, so 4B = 6G, or B/G = 6/4 = 3/2.

AI explanation

Using the method of alligation, the ratio of the number of boys to girls can be found from the differences between their individual means and the combined mean. The ratio is (combined mean minus girls mean) to (boys mean minus combined mean), which is (61 minus 55) to (65 minus 61). This results in a ratio of 6 to 4, simplifying to 3 : 2.

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