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In a class, the number of boys and girls are distinct. The average age

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In a class, the number of boys and girls are distinct. The average age  [#permalink]

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New post 17 Feb 2019, 22:35
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In a class, the number of boys and girls are distinct. The average age of all the student in the class equals the average of the average age of the boys and the average age of the girls. The sum of the average age of the boys and the average age of the girls is 10 years. Find the average age(in years) of the boys of the class?

A) 5 years
B) 3 years
C) 4 years
D) 2 years
E) 2.5 years
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Re: In a class, the number of boys and girls are distinct. The average age  [#permalink]

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New post 17 Feb 2019, 23:06
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This is a weighted average problem: in the question, we have two groups, boys and girls, and the question talks about the average ages of each group, and the average age of all of the children combined.

In general, in any weighted average problem, the average you get when you combine the groups will always be closer to the average of the larger group. For example, if you have men earning $40 per hour, and women earning $50 per hour at a company, then if there are more women than men at the company, the overall average wage will be closer to $50 than to $40 (so will be greater than $45). But here, we learn that the overall average age is exactly equal to the average of the average age of the boys and the average age of the girls, or in other words, it is exactly midway between them. That can only happen in one of two ways: either we have exactly equal numbers of boys and of girls, or the average age of the boys is identical to the average age of the girls. Since the question tells us the number of boys is different from the number of girls, then their average ages must be identical, and if they sum to 10, each group has an average age of 5.
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Re: In a class, the number of boys and girls are distinct. The average age  [#permalink]

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New post 18 Feb 2019, 00:45
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Let the Average age of class be T
Similarly let the average age of boys and girls be B & G respectively.
Now it is given that average age of total class is equal to average of boys and is also equal to average age of girls.
So,

T=B=G

Now it is given that B+G=10 also we know that B and G are equal so

putting that in the earlier equation we get both B and G are equal to 5.

If you think my reasoning is wrong please correct me :)
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Re: In a class, the number of boys and girls are distinct. The average age  [#permalink]

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New post 18 Feb 2019, 02:49
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vyascd wrote:
Now it is given that average age of total class is equal to average of boys and is also equal to average age of girls.


That is not given in the question (which is why my answer was so long :) ) - the question says that "The average age of all the student in the class equals the average of the average age of the boys and the average age of the girls." Using your notation, that means:

(B+G)/2 = T

and not that B = G = T (that is true here, because of other information in the question, but it's something you need to prove).
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Re: In a class, the number of boys and girls are distinct. The average age   [#permalink] 18 Feb 2019, 02:49
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