<PRE><B>Question 1102691</B>
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... and here is another solution using logical analysis -- similar to, yet very different from -- tutor ikleyn&#39;s second solution.&lt;br&gt;
This is a method I like to use when a problem is about averages of numbers that are all &quot;close together&quot;.&lt;br&gt;
The average of the 30 boys originally in the class is 15.&lt;br&gt;
After the 10 new boys join the class, the average of all 40 boys is 14; the average age went down by 1 year.&lt;br&gt;
On average, each of the 30 boys originally in the class is 1 year older than the new average; that means all together their ages are a total of 30 more than what is needed to make the new average.&lt;br&gt;
The total of the ages of the 10 new boys has to balance out those 30 &quot;extra&quot; years from the original 30 boys; that means the average age of the 10 new boys has to be 30/10 = 3 years LESS than the new average.&lt;br&gt;
Since the new average is 14, the average age of the 10 new boys is 14-3 = 11.&lt;br&gt;
With practice, this solution method is easy to use.  We can see how the method works by representing it symbolically, like this:&lt;br&gt;
(1) Let A be the new average.
(2) The sum of the ages of the original 30 boys in the class is {{{30(A+1) = 30A+30}}}.
(3) The new average, with 40 boys, is A; you want the total of the ages of all 40 boys to be {{{40A}}}.
(4) From (2) and (3), we see that the total of the ages of the 10 new boys has to be {{{40A - (30A+30) = 10A-30}}}.
(5) And that means the average age of the 10 new boys must be {{{(10A-30)/10 = A-3}}}
And since the new average is 14, the average age of the 10 new boys is 14-3 = 11.</PRE>