Question 1102691
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<pre>
Since "The average age of boys in a class of 30 is 15 years", the sum of their ages is 30*15 = 450 years.


Let N be the average age of 10 newcomers.  Then the sum of their ages is 10N.


The total sum of 30 + 10 boys is 450 + 10N, and their average age is {{{(450+10N)/(30+10)}}}.


So, from the condition you have this equation


{{{(450+10N)/40}}} = (15-1) = 14.


Then  450 + 10N = 14*40 = 560  ====>  10N = 560 - 450 = 110  ====>  N = {{{110/10}}} = 11.


<U>Answer</U>.  The average age of newcomers is 11 years.


<U>Check</U>.   {{{(30*15 + 11*10)/40}}} = 14.   ! Correct !
</pre>

Solved.



Or even simpler <U>logical analysis</U>:


<pre>
    Since "The average age of boys in a class of 30 is 15 years", the sum of their ages is 30*15 = 450 years.


    After joining 10 newcomers, the average age became 15-1 = 14 years;  hence, the sum of ages of all 40 students 
    of the class is 40*14 = 560 years now.


    The difference 560-450 = 110 years IS THE SUM of ages of the 10 newcomers.


    Hence, their average age is {{{110/10}}} = 11 years.
</pre>

You got the same answer.


Surely, this "logical analysis" is the same solution, simply presented in the wording form.