Question : The ratio of the number of men to the number of women in an office is 2 : 3. If the average weight of the men and the women in the office are 56 kg and 51 kg, respectively, find the average weight of the employees in the office (in kg).
Option 1: 53.5
Option 2: 54
Option 3: 53
Option 4: 54.5
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Correct Answer: 53
Solution :
Given: The ratio of the number of men to the number of women in an office is 2:3.
The average weights of the men and the women in the office are 56 kg and 51 kg.
Let the number of men be $2x$ and the number of women is $3x$.
So, the total weight of the men = $2x×56=112x$
Total weight of women = $3x × 51 = 153x$
Total weight of all the employees = $112x+153x=265x$
Total number of the employees = $2x+3x=5x$
Average weight of the employees = $\frac{265x}{5x}=53$ kg
Hence, the correct answer is 53.
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